I\'ve written an app that custom draws everything inside paint() based on fixed pixel positions. Then I disabled resize of the frame so its always visible.
However,
Not an expert, but you could just scale the Graphics2D object (the passed Graphics is in fact a Graphics2D instance), where the x and y ratios are the ratios of the fixed size you chose to draw and the actual size of the frame.
See http://download.oracle.com/javase/6/docs/api/java/awt/Graphics2D.html#scale%28double,%20double%29