Measure a piece of felt so that it is 4 - 6" larger than the completed puzzle plus a little extra on one side. Then take a cardboard tube left over from your giftwrap paper (the heavier the better) and wrap & glue (or sew) the longer end around the tube. Once dry roll up around tube and secure with rubber bands.
When I first found these instructions (probably over 5 years ago), there were pictures. But now they're just written instructions. Maybe if you search on the internet, you'll find photos (if that's important to you). http://organizedhome.com/sew-simple-gifts/jigsaw-puzzle-mat