For insulating materials (both solid and liquid), probing charge dynamics with microwaves is a part of dielectric spectroscopy.
Amongst the conductive materials, superconductors are a material class that is often studied with microwave spectroscopy, giving information about penetration depth (governed by the superconducting condensate), energy gap (single-particle excitation of Cooper pairs), and quasiparticle dynamics.
Another material class that has been studied using microwave spectroscopy at low temperatures are heavy fermion metals with Drude relaxation rates at GHz frequencies.