Agree that GannieRosie has good tips for getting as close to size as possible.
One other tip--maybe I am the last to figure this out!--is when I am sewing the "patched" 4 1/2" square to the 4 1/2" square of light or dark fabric, I line up the patched square's outside edge to the outside edge of the fabric square. This means any shortfall from my "patched" square is within the seam I am sewing (I sew a scant 1/4" from the edge of the fabric square and many times that will be less than 1/4" from the edge of the "patched" square that ended up say 4 1/8"). Hope that makes sense!