The influence of microwave resonance phenomena on complex refractive index in YIG plates has been theoretically and experimentally studied in the frequency range 26–38 GHz. It has been shown that a change in the magnetic field causes severe resonance-type changes in transmission and reflection factors. These changes are due both to effective interaction between millimeter electromagnetic waves and YIG plates (specifically, under ferromagnetic resonance conditions) and to the fulfillment of geometrical resonance conditions (when an integer number of half-waves or an integer odd number of quarter-waves are accommodated on the thickness of the plate). An algorithm to calculate complex refractive index with regard to the tensor-type magnetic permeability of YIG is suggested. The field and frequency dependences of complex refractive index have been analyzed. Geometrical resonance fields have been compared with extrema in the field dependences of the transmission and reflection factor moduli.