You can call the following method:

   table.getTableHeader().setResizingAllowed(false);

However, be aware that this will disable resizing for all columns, and will still resize the columns proportionally when resizing the container in which the JTable is hosted. To fix the size of one column, you have to think about what behavior you want and override the method sizeColumnsToFit().

Main.java:

import javax.swing.table.*;
import java.awt.event.*;
import javax.swing.*;
import java.util.*;
import java.awt.*;
 
public class Main extends JFrame {
   public Main() {
      super("TableModel Demonstration");
 
      // create our own custom TableModel
      WineTableModel wineModel = new WineTableModel();
      JTable table = new JTable(wineModel);
 
      // add rows to our TableModel, each row is represented as a Wine object
      wineModel.addWine(new Wine("Chateau Meyney, St. Estephe", "1994", 18.75f, true));
      wineModel.addWine(new Wine("Chateau Montrose, St. Estephe", "1975", 54.25f, true));
      wineModel.addWine(new Wine("Chateau Gloria, St. Julien", "1993", 22.99f, false));
      wineModel.addWine(new Wine("Chateau Beychevelle, St. Julien", "1970", 61.63f, false));
      wineModel.addWine(new Wine("Chateau La Tour de Mons, Margeaux", "1975", 57.03f, true));
      wineModel.addWine(new Wine("Chateau Brane-Cantenac, Margeaux", "1978", 49.92f, false));
 
 
      // don't allow resizing columns
      table.getTableHeader().setResizingAllowed(false);
 
 
      // create the scroll pane and add the table to it. 
      JScrollPane scrollPane = new JScrollPane(table);
 
      // add the scroll pane to this window.
      getContentPane().add(scrollPane, BorderLayout.CENTER);
 
      addWindowListener(new WindowAdapter() {
         public void windowClosing(WindowEvent e) {
            System.exit(0);
         }
      });
   }
 
   public static void main(String[] args) {
      Main main = new Main();
      main.pack();
      main.setVisible(true);
   }
}
 
// a simple object that holds data about a particular wine
class Wine {
   private String  name;
   private String  vintage;
   private float   price;
   private boolean inStock;
 
   public Wine(String name, String vintage, float price, boolean inStock) {
      this.name = name;
      this.vintage = vintage;
      this.price = price;
      this.inStock = inStock;
   }
 
   public String getName()     { return name; }
   public String getVintage()  { return vintage; }
   public float  getPrice()    { return price; } 
   public boolean getInStock() { return inStock; }
 
   public String toString() { 
      return "[" + name + ", " + vintage + ", " + price + ", " + inStock + "]"; }
}
 
class WineTableModel extends AbstractTableModel {
   // holds the strings to be displayed in the column headers of our table
   final String[] columnNames = {"Name", "Vintage", "Price", "In stock?"};
 
   // holds the data types for all our columns
   final Class[] columnClasses = {String.class, String.class, Float.class, Boolean.class};
 
   // holds our data
   final Vector data = new Vector();
  
   // adds a row
   public void addWine(Wine w) {
      data.addElement(w);
      fireTableRowsInserted(data.size()-1, data.size()-1);
   }
 
   public int getColumnCount() {
      return columnNames.length;
   }
         
   public int getRowCount() {
      return data.size();
   }
 
   public String getColumnName(int col) {
      return columnNames[col];
   }
 
   public Class getColumnClass(int c) {
      return columnClasses1;
   }
 
   public Object getValueAt(int row, int col) {
      Wine wine = (Wine) data.elementAt(row);
      if (col == 0)      return wine.getName();
      else if (col == 1) return wine.getVintage();
      else if (col == 2) return new Float(wine.getPrice());
      else if (col == 3) return new Boolean(wine.getInStock());
      else return null;
   }
 
   public boolean isCellEditable(int row, int col) {
      return false;
   }
}

Write your own cell renderer. This example colors all rows green where the price of
the wine is < 55, red otherwise.

Main.java:

import javax.swing.table.*;
import java.awt.event.*;
import javax.swing.*;
import java.util.*;
import java.awt.*;
 
public class Main extends JFrame {
   public Main() {
      super("TableModel Demonstration");
  
      // create our own custom TableModel
      WineTableModel wineModel = new WineTableModel();
      JTable table = new JTable(wineModel);
 
      // since we’re using values of floats and boolean here, we need
      // to set the cell renderer for every column. 
      for (int i =0; i<wineModel.getColumnCount();i++) {
         table.setDefaultRenderer(table.getColumnClass(i), new WineCellRenderer());
      }
       
      // add rows to our TableModel, each row is represented as a Wine object
      wineModel.addWine(new Wine("Chateau Meyney, St. Estephe", "1994", 18.75f, true));
      wineModel.addWine(new Wine("Chateau Montrose, St. Estephe", "1975", 54.25f, true));
      wineModel.addWine(new Wine("Chateau Gloria, St. Julien", "1993", 22.99f, false));
      wineModel.addWine(new Wine("Chateau Beychevelle, St. Julien", "1970", 61.63f, false));
      wineModel.addWine(new Wine("Chateau La Tour de Mons, Margeaux", "1975", 57.03f, true));
      wineModel.addWine(new Wine("Chateau Brane-Cantenac, Margeaux", "1978", 49.92f, false));
 
      // create the scroll pane and add the table to it. 
      JScrollPane scrollPane = new JScrollPane(table);
 
      // add the scroll pane to this window.
      getContentPane().add(scrollPane, BorderLayout.CENTER);
 
      addWindowListener(new WindowAdapter() {
         public void windowClosing(WindowEvent e) {
            System.exit(0);
         }
      });
   }
 
   public static void main(String[] args) {
      Main main = new Main();
      main.pack();
      main.setVisible(true);
   }
}
 
// a simple object that holds data about a particular wine
class Wine {
   private String  name;
   private String  vintage;
   private float   price;
   private boolean inStock;
 
   public Wine(String name, String vintage, float price, boolean inStock) {
      this.name = name;
      this.vintage = vintage;
      this.price = price;
      this.inStock = inStock;
   }
 
   public String getName()     { return name; }
   public String getVintage()  { return vintage; }
   public float  getPrice()    { return price; } 
   public boolean getInStock() { return inStock; }
 
   public String toString() { 
      return "[" + name + ", " + vintage + ", " + price + ", " + inStock + "]"; }
}
 
class WineTableModel extends AbstractTableModel {
   // holds the strings to be displayed in the column headers of our table
   final String[] columnNames = {"Name", "Vintage", "Price", "In stock?"};
 
   // holds the data types for all our columns
   final Class[] columnClasses = {String.class, String.class, Float.class, Boolean.class};
 
   // holds our data
   final Vector data = new Vector();
  
   // adds a row
   public void addWine(Wine w) {
      data.addElement(w);
      fireTableRowsInserted(data.size()-1, data.size()-1);
   }
 
   public int getColumnCount() {
      return columnNames.length;
   }
         
   public int getRowCount() {
      return data.size();
   }
 
   public String getColumnName(int col) {
      return columnNames[col];
   }
 
   public Class getColumnClass(int c) {
      return columnClasses1;
   }
 
   public Object getValueAt(int row, int col) {
      Wine wine = (Wine) data.elementAt(row);
      if (col == 0)      return wine.getName();
      else if (col == 1) return wine.getVintage();
      else if (col == 2) return new Float(wine.getPrice());
      else if (col == 3) return new Boolean(wine.getInStock());
      else return null;
   }
 
   public Object getValueAtRow(int row) {
      Wine wine = (Wine) data.elementAt(row);
      return wine;
   }
 
   public boolean isCellEditable(int row, int col) {
      return false;
   }
}
 
class WineCellRenderer extends DefaultTableCellRenderer {
   public Component getTableCellRendererComponent(
            JTable table, Object value, boolean isSelected,
            boolean hasFocus, int row, int column)
   {
      WineTableModel wtm = (WineTableModel) table.getModel();
      Wine wine = (Wine) wtm.getValueAtRow(row);
 
      if (wine.getPrice() < 55) {
         setBackground(Color.green);
      }
      else {
         setBackground(Color.red);
      }
 
      return super.getTableCellRendererComponent(table, value, isSelected, 
                                                 hasFocus, row, column);
   }
}

The easiest way is to use HTML in your text, check How do I create a JLabel with the text underlined?

But here’s a code sample that does not make use of the HTML feature. It underlines all Integers in the JTable whose values are between 1970 and 1980.

Main.java:

import javax.swing.table.*;
import java.awt.event.*;
import javax.swing.*;
import java.awt.*;
 
public class Main extends JFrame 
{
   public Main() {
      super("Table example, Wines from Bordeaux");
 
      Object[][] tabledata = {
            { "Chateau Meyney, St. Estephe", 	   new Integer(1994), "$18.75"},
            { "Chateau Montrose, St. Estephe", 	   new Integer(1975), "$54.25" },
            { "Chateau Gloria, St. Julien", 	   new Integer(1993), "$22.99" },
            { "Chateau Beychevelle, St. Julien",   new Integer(1970), "$61.63" },
            { "Chateau La Tour de Mons, Margeaux", new Integer(1975), "$57.03" },
            { "Chateau Brane-Cantenac, Margeaux",  new Integer(1978), "$49.92" },
      };
 
      String columnheaders[] = { "Wine", "Vintage", "Price" };
 
      JTable table = new JTable(tabledata, columnheaders);
      table.setPreferredScrollableViewportSize(new Dimension(500, 70));
 
      UnderlineTableCellRenderer renderer = new UnderlineTableCellRenderer();
      table.setDefaultRenderer(Object.class, renderer);
      table.setRowHeight(30);
 
      JScrollPane scrollPane = new JScrollPane(table);
      getContentPane().add(scrollPane);
 
      addWindowListener(new WindowAdapter() {
         public void windowClosing(WindowEvent we) {
            System.exit(0);
         }
      });
 
      pack();
   }
 
   public static void main(String []args) {
      Main main = new Main();
      main.show();
   }
}
 
class UnderlineTableCellRenderer extends DefaultTableCellRenderer 
{
   public Component getTableCellRendererComponent(JTable table, Object value, boolean isSelected,
                                                  boolean hasFocus, int row, int column) {
      if (value instanceof Integer) {
         Integer amount = (Integer) value;
         if (amount.intValue() > 1970 && amount.intValue() < 1980) {
            return new UnderlinedJLabel("" + amount.intValue());
         }
      }
 
      return super.getTableCellRendererComponent
                      (table, value, isSelected, hasFocus, row, column);
   }
}
 
class UnderlinedJLabel extends JLabel
{
   public UnderlinedJLabel() {
   }
 
   public UnderlinedJLabel(Icon image) {
      super(image);
   }
 
   public UnderlinedJLabel(Icon image, int horizontalAlignment) {
      super(image, horizontalAlignment);
   }
 
   public UnderlinedJLabel(String text) {
      super(text);
   }
 
   public UnderlinedJLabel(String text, Icon icon, int horizontalAlignment) {
      super(text, icon, horizontalAlignment);
   }
 
   public UnderlinedJLabel(String text, int horizontalAlignment) {
      super(text, horizontalAlignment);
   }
 
   public void paint(Graphics g) {
      super.paint(g);
      underline(g);
   }
 
   protected void underline(Graphics g) {
      Insets insets = getInsets();
      FontMetrics fm = g.getFontMetrics();
      Rectangle textR = new Rectangle();
      Rectangle viewR = new Rectangle(
                                  insets.left, 
                                  insets.top, 
                                  getWidth() - (insets.right + insets.left), 
                                  getHeight() - (insets.bottom + insets.top));
  
      // compute and return location of the icons origin,
      // the location of the text baseline, and a possibly clipped
      // version of the compound label string.  Locations are computed 
      // relative to the viewR rectangle.
      String text = SwingUtilities.layoutCompoundLabel(
                         this,                        // this JLabel
                         fm,                          // current FontMetrics
                         getText(),                   // text
                         getIcon(),                   // icon
                         getVerticalAlignment(),      
                         getHorizontalAlignment(),
                         getVerticalTextPosition(),
                         getHorizontalTextPosition(), 
                         viewR,                       
                         new Rectangle(),             // don't care about icon rectangle
                         textR,                       // resulting text locations
                         getText() == null ? 0 : ((Integer)UIManager.get("Button.textIconGap")).intValue());
 
      // draw line
      int textShiftOffset = ((Integer) UIManager.get("Button.textShiftOffset")).intValue();
      g.fillRect(textR.x +
                 textShiftOffset - 4,
                 textR.y + fm.getAscent() + textShiftOffset + 2,
                 textR.width, 
                 1);
   }
}