Try smaller glasses with lenses that aren't so large that they make you look bug-eyed. Bigger glasses will overpower your face, and even if you're craving the huge lens celebrity look, medium frames work better with a smaller face.
Try on a pair of sunglasses with incomplete frames. Choose glasses where the frame connects to the lens at or above the temple and ends at the bridge of the nose, leaving the bottom of the lens frameless. Hard, thick lines are going to make you look square.
Slip on a pair of cat-eye sunglasses. The pointed edges and gentle curves will work with your strict facial lines for a fabulous finish.
Look for glasses with oval frames. They have a softer curve than cat-eyes and look a little less trendy. They're great for a classic look.
Try sunglasses that have the arms attached at or above the level of your temples. Cat-eyes or ovals with outer points above temple-level will gentle a strong, square face.