Would be a quick and easy way to drop a transponder on an asteroid. Something that would give off a radio signal. Wouldn't have to be much of one, depending on the quality of the receivers down here (look at the signal strength of the Pioneer, for example.)

Design of the transponder is easy. I'd use a small plutonium generator, so solar distance wasn't an issue. Design the case to withstand a reasonable impact (you don't want to hit to hard, since even an indestructible package might bury itself uselessly in the dirt).

You can stick science instruments on it if you get ambitious, but the idea is to put something on the asteroid that tells you EXACTLY where it is and what its velocity is. Unlike subatomic particles, Heisenberg doesn't keep you from knowing both of these for asteroids.

Big trick of course is the propulsion to launch it and make the rendezvous. If it were me, I'd build a big honking probe with ion propulsion, carrying a dozen or so of these transponders, and have it stroll merrily through the Solar System dropping them off over a decade or so.

Tag NEOs as they're discovered. Even a laser retroreflector would be better than nothing.