References: BFO metal detector, Magnetic Field Measurement, Teardown.
First thing, I should be to recreate what has been done, once I have a good understanding of the principles I could customize the design. One coil emits and the other coil receives, there is a larger refection when a metal is present.
Magnetometers are very sensitive MEMS devices, I wonder if you can attach an external antenna to one of those.