General

How about getting a new boyfriend?

Satisfy his worries at the store. Microwaves can and do leak so when you're at the store place your phone inside that microwave and close it. Then try to call the phone, if it gets no signal that means the microwave is sufficiently insulated and will not leak.

Fashion him a tinfoil hat and pants to protect his brain and nads when standing near the microwave.

Some microwave ovens can leak, but this is rare, and there are inexpensive detectors that can be bought to prevent this. Microwave radiation is non-ionising: the only danger to people is that it can cook one from the inside. If he is worried, just get one of the detectors.

Incidentally, I recommend the Panasonic microwave ovens that have an inverter.