One of the secrets to a good looking binding is trimming just a sliver of fabric from the edges, using a strajght ruler all along one side of the placemat at once, to get rid of bumps. threads and dips. This makes the sewing much easier!
Then pin the binding edge exactly on top of the placemat edge. When you sew, try to keep the width of the seam even.
Then when you turn it, the binding will fit around the edge underneath it surprisingly nicely. Good luck! JP