To get the size of a (realised) JComponent, then call getSize() on it.
It will return a Dimension containing pixel size, let us call that d1.
Now suppose the dimension (in pixels) of your screen or display area
(printout) is d2.

Now, I'm assuming you want conservative scaling, i.e. you can see all of
the component on the screen, and you wish to maintain the aspect ratio...

Work out the width/height ratio of the two dimensions:

r1 = (float)d1.getWidth()/(float)d1.getHeight();
r2 = (float)d2.getWidth()/(float)d2.getHeight();

Now you examine these two ratios to decide whether to scale your graphic
to fit on the X or the Y scale:

float scaleFactor = 1;
if (r1 > r2) {
 // we need to scale by the width of the
 // component, as it is proportionally wider/fatter than
 // the screen area
 scaleFactor = (float)d2.getWidth() / (float)d1.getWidth();
}
else {
 // we need to scale by the height of the
 // component, as it is proportionally taller than
 // the screen area
 scaleFactor = (float)d2.getHeight() / (float)d1.getHeight();
}

Then set the scaleFactor on the Graphics2D object before rendering:

g2d.setScale(scaleFactor, scaleFactor);

I've not actually tested this code, but you get the idea...
alex