I can feel your pain on this one. I have 2 little sweethearts that have me do their quilting. Yes, their borders wave like there is no tomorrow. I use beadboard or piano key on the borders. I cut another piece of batting and place it under the borders of the quilt and then quilt. I do not baste the edge until after the quilting so that I can manipulate the fabric. If there is just a bit of wave to the borders, I do not add the additional batt but do beadboard about 1 inch apart. This usually will take care of the waves. When using the additional batt then I beadboard about 1 1/4 to 1 1/2 inch apart. Good luck and hope this helps.