This work was supported in part by the TEAM-TECH Project titled "High-precision techniques of millimeter and sub-THz band characterization of materials for microelectronics" operated within the Foundation for Polish Science TEAM TECH Programme co-financed by the European Regional Development Fund, Operational Programme Smart Growth 2014–2020; in part by the European Metrology Programme for Innovation and Research (EMPIR), under 18SIB09-TEMMT project (EMPIR programme is co-financed by the Participating States and from the European Union's Horizon 2020 Research and Innovation Programme); and in part by the Warsaw University of Technology within the Internal Project "Light-matter interaction." of dielectric micro-resonators with microwave photons in a Fabry–Perot open resonator.

Measurement results of uniaxially anisotropic materials performed with the aid of a plano-concave Fabry–Perot open resonator in the 20–50 GHz frequency range are presented and discussed in this letter. It is shown that a linear polarization of Gaussian modes applied in the characterization allows extracting in-plane complex permittivity of such materials as crystals and foils in a single measurement cycle. It is also shown that dielectric losses exhibit anisotropy, which can be quite significant, like in the sapphire, or relatively small, like in polymer foils.