This idea might be patented, so it might not be suitable for a commercial project, but you can actually measure the position and orientation of one electronic device relative to another, with reasonable accuracy, using magnetic fields. This is how Polhemus and Ascension trackers work. They are used in VR motion tracking, and in surgery for tracking the position of surgical instruments during operations.
The basic concept is to have one set of coils transmitting, and another receiving. The transmitter coils emit audio frequency alternating magnetic fields, and the receiver coils then measure the amplitude of the fields in the three receiver coils.
There is some code available online for doing these calculations. You might also take a look at the guy's project page: Open source electromagnetic trackers using OpenIGTLink.
This may not be quite the system you're looking for, as it's fairly complex, and is giving you much more info than you wanted. However, a simpler algorithm could be used which just gave you distance.
A company called Sixense make a gaming controller with a 6DOF sensor in it. I don't know how easy it would be to integrate this technology into your project though.
Update:
Now that I know what your application is, I have been thinking of a very similar application. My suggestion would be this:
Use the three orthogonal coils approach. Both the mother and child have a set of coils. The child would be the transmitter. Every few seconds, the child module would transmit an acoustic frequency magnetic field on each coil in turn. The mother module would measure the amplitude of the voltage induced in its coils. If the amplitude was too low, or if no signal was heard for more than a few seconds, then the alarm sounds.
Consider using a string pot.
http://www.celesco.com/faq/cet.htm
Otherwise, to stick with your original idea, you could possibly use a transponder based ultrasound system. You would have an ultrasound transceiver on the box, and a transponder on the ground. Periodically, the transceiver would send out an ultrasound burst. The transponder on the ground would detect and reply. The round trip time is proportional to the distance. If you need extreme accuracy, you would want to somehow adjust for temperature. The speed of sound is affected by temperature (and pretty much only by temperature).
Good luck!
Best Answer
Have you given any thought to LVDT (linear variable differential transformer) devices? It's been 20 years since I used them and you could get sub 30 mm devices with raw 10-bit resolution.
We measured over a 4 mm range, it was mechanically and electrically noisy and with oversampling 1 um resolution/repeatability was achieved. Processing and analogue was difficult back then, now it would be immensely simple. May just revisit it again just to see.