While I muck about with TextLayout, you could just use the Graphics context's FontMetrics, for example...

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.EventQueue;
import java.awt.Font;
import java.awt.FontMetrics;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.font.FontRenderContext;
import java.awt.font.TextLayout;
import java.awt.geom.Rectangle2D;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.UIManager;
import javax.swing.UnsupportedLookAndFeelException;
public class LayoutText {
    public static void main(String[] args) {
        new LayoutText();
    }
    public LayoutText() {
        EventQueue.invokeLater(new Runnable() {
            @Override
            public void run() {
                try {
                    UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());
                } catch (ClassNotFoundException | InstantiationException | IllegalAccessException | UnsupportedLookAndFeelException ex) {
                }
                JFrame frame = new JFrame("Testing");
                frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                frame.setLayout(new BorderLayout());
                frame.add(new TestPane());
                frame.pack();
                frame.setLocationRelativeTo(null);
                frame.setVisible(true);
            }
        });
    }
    public class TestPane extends JPanel {
        private String text;
        public TestPane() {
            text = "Along time ago, in a galaxy, far, far away";
        }
        @Override
        public Dimension getPreferredSize() {
            return new Dimension(200, 200);
        }
        @Override
        protected void paintComponent(Graphics g) {
            super.paintComponent(g);
            Graphics2D g2d = (Graphics2D) g.create();
            g2d.setColor(Color.RED);
            g2d.drawLine(getWidth() / 2, 0, getWidth() / 2, getHeight());
            g2d.drawLine(0, getHeight() / 2, getWidth(), getHeight() / 2);
            Font font = new Font("Arial", Font.BOLD, 48);
            g2d.setFont(font);
            FontMetrics fm = g2d.getFontMetrics();
            int x = ((getWidth() - fm.stringWidth(text)) / 2);
            int y = ((getHeight() - fm.getHeight()) / 2) + fm.getAscent();
            g2d.setColor(Color.BLACK);
            g2d.drawString(text, x, y);
            g2d.dispose();
        }
    }
}
Okay, after some fussing about...
Basically, text rendering occurs at the baseline, this makes the y position of the bounds usually appear above this point, making it look like the text is been painted above the y position
To overcome this, we need to add the font's ascent minus the font's descent to the y position...
For example...
FontRenderContext context = g2d.getFontRenderContext();
Font font = new Font("Arial", Font.BOLD, 48);
TextLayout txt = new TextLayout(text, font, context);
Rectangle2D bounds = txt.getBounds();
int x = (int) ((getWidth() - (int) bounds.getWidth()) / 2);
int y = (int) ((getHeight() - (bounds.getHeight() - txt.getDescent())) / 2);
y += txt.getAscent() - txt.getDescent();
... This is why I love rendering text by hand ...
Runnable example...

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.EventQueue;
import java.awt.Font;
import java.awt.FontMetrics;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.font.FontRenderContext;
import java.awt.font.TextLayout;
import java.awt.geom.Rectangle2D;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.UIManager;
import javax.swing.UnsupportedLookAndFeelException;
public class LayoutText {
    public static void main(String[] args) {
        new LayoutText();
    }
    public LayoutText() {
        EventQueue.invokeLater(new Runnable() {
            @Override
            public void run() {
                try {
                    UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());
                } catch (ClassNotFoundException | InstantiationException | IllegalAccessException | UnsupportedLookAndFeelException ex) {
                }
                JFrame frame = new JFrame("Testing");
                frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                frame.setLayout(new BorderLayout());
                frame.add(new TestPane());
                frame.pack();
                frame.setLocationRelativeTo(null);
                frame.setVisible(true);
            }
        });
    }
    public class TestPane extends JPanel {
        private String text;
        public TestPane() {
            text = "Along time ago, in a galaxy, far, far away";
        }
        @Override
        public Dimension getPreferredSize() {
            return new Dimension(200, 200);
        }
        @Override
        protected void paintComponent(Graphics g) {
            super.paintComponent(g);
            Graphics2D g2d = (Graphics2D) g.create();
            g2d.setColor(Color.RED);
            g2d.drawLine(getWidth() / 2, 0, getWidth() / 2, getHeight());
            g2d.drawLine(0, getHeight() / 2, getWidth(), getHeight() / 2);
            FontRenderContext context = g2d.getFontRenderContext();
            Font font = new Font("Arial", Font.BOLD, 48);
            TextLayout txt = new TextLayout(text, font, context);
            Rectangle2D bounds = txt.getBounds();
            int x = (int) ((getWidth() - (int) bounds.getWidth()) / 2);
            int y = (int) ((getHeight() - (bounds.getHeight() - txt.getDescent())) / 2);
            y += txt.getAscent() - txt.getDescent();
            g2d.setFont(font);
            g2d.setColor(Color.BLACK);
            g2d.drawString(text, x, y);
            g2d.setColor(Color.BLUE);
            g2d.translate(x, y);
            g2d.draw(bounds);
            g2d.dispose();
        }
    }
}
Take a look at Working with Text APIs for more information...
Updated
As has already been suggested, you could use a GlyphVector...
Each word (Cat and Dog) is calculated separatly to demonstrate the differences

import java.awt.BorderLayout;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.EventQueue;
import java.awt.Font;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.font.FontRenderContext;
import java.awt.font.GlyphVector;
import java.awt.geom.Rectangle2D;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.UIManager;
import javax.swing.UnsupportedLookAndFeelException;
public class LayoutText {
    public static void main(String[] args) {
        new LayoutText();
    }
    public LayoutText() {
        EventQueue.invokeLater(new Runnable() {
            @Override
            public void run() {
                try {
                    UIManager.setLookAndFeel(UIManager.getSystemLookAndFeelClassName());
                } catch (ClassNotFoundException | InstantiationException | IllegalAccessException | UnsupportedLookAndFeelException ex) {
                }
                JFrame frame = new JFrame("Testing");
                frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                frame.setLayout(new BorderLayout());
                frame.add(new TestPane());
                frame.pack();
                frame.setLocationRelativeTo(null);
                frame.setVisible(true);
            }
        });
    }
    public class TestPane extends JPanel {
        private String text;
        public TestPane() {
            text = "A long time ago, in a galaxy, far, far away";
        }
        @Override
        public Dimension getPreferredSize() {
            return new Dimension(200, 200);
        }
        @Override
        protected void paintComponent(Graphics g) {
            super.paintComponent(g);
            Graphics2D g2d = (Graphics2D) g.create();
            g2d.setColor(Color.RED);
            g2d.drawLine(getWidth() / 2, 0, getWidth() / 2, getHeight());
            g2d.drawLine(0, getHeight() / 2, getWidth(), getHeight() / 2);
            Font font = new Font("Arial", Font.BOLD, 48);
            g2d.setFont(font);
            FontRenderContext frc = g2d.getFontRenderContext();
            GlyphVector gv = font.createGlyphVector(frc, "Cat");
            Rectangle2D box = gv.getVisualBounds();
            int x = 0;
            int y = (int)(((getHeight() - box.getHeight()) / 2d) + (-box.getY()));
            g2d.drawString("Cat", x, y);
            x += box.getWidth();
            gv = font.createGlyphVector(frc, "Dog");
            box = gv.getVisualBounds();
            y = (int)(((getHeight() - box.getHeight()) / 2d) + (-box.getY()));
            g2d.drawString("Dog", x, y);
            g2d.dispose();
        }
    }
}