A review of the measurement methods of the basic electromagnetic parameters of gyromagnetic materials at microwave frequencies is presented. Measurement methods of the complex permittivity, the complex initial permeability, the intrinsic permeability tensor components and the ferromagnetic linewidth are considered. A large part of the paper is devoted to the description and analysis of the rigorous electrodynamic methods for extraction of the measured parameters from the raw measurement data. Four groups of gyromagnetic materials are considered: microwave magnetic absorbers, polycrystalline ferrites, low loss monocrystalline garnets and thin metallic ferromagnetic films. Measurement fixtures include resonant and non-resonant fixtures, employing resonance cavities, dielectric resonators and sections of transmission lines. A rigorous electrodynamic approach to data analysis allows us to improve the accuracy of the measurements to compare them to the commonly used perturbation methods.