I haven't tried this technique yet, sounds interesting.

Living in a city where phone-snatching thieves are widely reported on built my habit of memorising the next couple steps quickly (e.g. 2nd street on the left, then right by the station), then looking out for them without the map. North-Up helps anyways because you don't have to separately figure out which erratic direction the magnetic compass has picked this time (maybe it's to do with the magnetic stuff I EDC.)