About 12 years ago I had to design a piece of test equipment to emulate 400W of audio into a programmable array of dynamically switched 50W "speaker" loads, with programmable crossovers too. Obviously, using real speakers was not practical.
I don't have the circuit now, but I recall a decent single voice coil speaker emulator was more than just an RLC circuit; it was an array of R's, L's and C's for each speaker. Maybe 8 or so passives for each speaker.
A microphone emulator could be similar but on a much smaller scale and not emulated by a simple RLC circuit either, but could be approximated in a model. The technology in the microphone needs to be known. Eg: electret/crystal/voice coil/
In practical terms, assuming it is a voice coil microphone, you could use a complex impedance meter assuming the L is quite prominent over the C and you know the R. ie: work back to get the L. It will only be an approximate.