I have a bunch of different ways I use to make maps for my tabletop game. Sometimes I draw one on graph paper. Sometimes I use Dungeonographer. Sometimes I copy a map from a published adventure or use the donjon random generators. These all have the same output: a piece of paper (or maybe two) with a map on it, and the map is usually quarter inch squares, or so.
When it's time to put minis on a mat, though, I need to copy over the relevant details of the map to our battle mat. (We use Tact-Tiles.) This is fine when most of our map is overland detail and I'm just copying down one or two rooms in which combat will occur. For dungeon crawls, where there are more random encounters or where combat can chase through many rooms, it can lead to a pretty tedious drawing of the whole dungeon as we go.
I feel foolish for having to ask, but is there some trick, technique, or something to make it less tedious to transcribe maps from printed pages to the battle mat?
EDIT: Answers in general are great, but I should note that the best answers, for me, will be informed by this previously-unmentioned fact: the game venue is not my house, so I have limited prep time on site.