These water-soluble overhead-projection pens work well with the mats. The black, blue, and green colors are the best regarding being removed with water. The red has a tendency of staining much more than the other colors so it is best used for highlighting only.
NOTE: Never use dry erase, permanent, or grease-pencil markers. The vinyl is too porous for the lines created from them to be able to be removed. If you have any doubt of the suitability of any particular marker, draw a small line on the border, let sit for awhile, and see how well it can be removed. Better to have a small permanent blemish on the edge of the mat than a permanent map drawn on the entirety of the mat!