There are a few types of circuits that cause some LEDs to light up whenever it senses a transmission signal. One version doesn't even require a battery. It is a small PCB with 2 sets of tracks, long enough to act as an antenna/inductor. One track connects to the gate of a SMD transistor, the other track connects to the source terminal of the transistor. The drain terminal connects to the LED which appears to connect back to the first track. This version needs to be practically sitting on the phone's antenna to work. As the phone transmits, the 2 tracks charge up. When a certain threshold is reached, the first track has enough energy to activate the transitor and allow the second track to discharge in to the LED. This can happen so fast that the LED appears to stay lit.
I have something like the necklace, except mine is a hand-shape to hold the phone when you're at home. It uses a battery, but I suppose the basic principle is similar to the first circuit, the battery being there to provide power to make it more sensitive. And also, there are 5 LEDs which blink in sequence, which, I'm guessing are also powered by the battery.
I haven't tried the microwave thing yet, but I can already imagine what my wife is going to say. /ubbthreads/images/graemlins/crazy.gif