Curvy lines are your friend. Balance the angles of your face with feminine hats that have wide, floppy brims and rounded crowns. A shorter brim will only make your face look wider, and a stiff brim will result in too much harshness all over. The straight lines of the hat plus the straight lines of your face will make your portrait look a bit too severe.
Before you step in front of the camera, make sure your hat rests directly on top of your head. If it's toward the back, it will pronounce the sharper features of your face and may even make your face appear wider and larger. Misplaced accessories can make even the most gorgeous face look less than appealing.
Wear the hat at an angle for a picture-perfect pose. Doing this breaks up the lines of your face and softens the overall look. Tilt the hat to the side or slightly to the front to ensure the fiercest of looks.
Sun hats and straw hats in particular will look fantastic on you. Berets and newsboy caps will work as long as you wear them at the hairline -- tilt them if you can. Beanie caps are not the best choice for you. Celebrities have been seen everywhere wearing fedoras and Panama hats; you can pull off this look too -- just check that the crown isn't too pointed or narrow.