If you sewed the borders on without first measuring the quilt through the middle and cutting the border strips to match that measurement, that is why you have the ripples. You have sewn extra border fabric to the quilt, creating ripples. You will need to remove the border strips, measure, and cut border strips to correct length. Then fold border piece in half and half again, pin border to quilt at middle, ends, and halfway points -- all before you ever start sewing the border to the quilt. Ease any excess to keep the pins matching.
Oops. Just saw your post about only one border being rippled on the outside. Either the outside edge of the border stretched while being handled, or you have sewn excess border to the quilt. You can try "blocking" the border edge to see if you can get it to shrink back to correct length. Sharon Schamber has a Youtube video on how to do this for a block. Basically you pin the fabric to an ironing board, spray with spray starch, and steam the fabric back into shape.