My strategy for square images...
4 1/2" square image on 5x7 paper with an 8x10 mat
6 1/2" square image on 8x10 paper with an 11x14 mat
9" square image on 11x14 paper with a 16x20 mat
In each case, the top and two side borders of the mat are equal in size. Thus, the bottom border is larger.
I like this progression of image sizes, because each is roughly twice as large in area as the next smaller size. This is pretty much the same relationship as between the traditional rectangular sizes, i.e. 5x7, 8x10 and 11x14.
The downside is that custom mats are required. However, it makes for an elegant presentation.