How, specifically, does an electric meter measure wattage?

Good one Lefty!

I can think of a couple of other possibilities off hand. If you only need a little power, just wrap some wires around one leg of the incoming before the meter and suck some power out inductively. The other one is to use something that has a very low power factor and returns everything back to the power company as reflected power. I used to do this with a fluorescent tube, just connect the ends without turning on the filaments then strike a spark with something else to get it to fire up and away you go, free light. You can also heat the filaments with a battery and get it to fire and disconnect the battery; big battery though.

A long, long time ago with completely different meters than we have today, we would use a really powerful magnet and retard the aluminum disk by putting the magnet right up against the meter's glass and holding it on with duct tape. This wouldn't stop the meter, but it would slow it down noticeably. Doesn't work with any of the new meters though.

You could also slip a bribe to the guy that reads the meter.