How to mesure distance between two objects?
I've seen three basic options for distance measurement: triangulation, measuring power drop from a source of known power, and measuring travel time for a signal of known velocity.

Signal power drop is an issue over 10 meters because of the inverse square law: if a signal can be detected 10m away, it's going to be 10000x stronger at a distance of 10 cm. For magnetic fields, for example, that's a difference between 60 uT (about the Earth's magnetic field) and 6 T (a very very strong magnet, which would rip the metal off anything nearby). You might could use RF power drop, but I expect that there would be similar safety issues, not to mention the FCC coming down on you like a ton of bricks.

You've got two basic options for timing signal propagation: sound, and EM fields. EM fields can't really give you the precision you want using travel time as your distance measurement, because 1 mm is about 3 picoseconds at the speed of light. I could be wrong, but that's orders of magnitude beyond what's a reasonable granularity for timing measurements with any hardware I've ever seen.

Sound is easier to work with, but can't really propagate at the distances you're talking about at frequencies over about 250 kHz. (http://www.katho.be/apps.aspx?smid=2688) The wavelength of 250 kHz is about 1.4 mm, so no one microphone is going to give you an arrival time down to the precision you want. Possibly some sort of interferometer? Not to mention that those high frequencies aren't going to work so well without line of sight.

Your best bet is probably triangulation. That requires three locations, not two, and might give you acceptable results if a third station is something you can work with. That changes the question to: how do I determine the direction to something, when it might change location by 1mm 10 meters away, giving a needed precision of five thousandths of a degree?

I'm afraid I don't know the answer to that one. :)