I mark the cutting line with a Sharpie first, then stitch around the quilt edge with a large basting stitch -- usually just a little inside that marked Sharpie line.
Next I sew my binding on, raw edges of the binding lined up with the Sharpie marked line.
Last, I cut the quilt sandwich on the marking line (or adjust the cutting a little to one side of the line or the other, depending if I want a little more or less inside the binding).
All of these things help me keep from stretching either the quilt or the binding.
Oh, and I also heavily starch the binding fabric before I cut the binding strips; this keeps the folded binding stable while I am handling it and also helps prevent it from stretching.