In this work, a circular microwave waveguide with an anisotropic medium was investigated, and the dependences of the radiation of an antenna system from a microwave circular anisotropic waveguide for various types of electromagnetic waves were determined. New mathematical models of the microwave electromagnetic field of a circular anisotropic waveguide have been developed. The electrodynamic dependences of the modulus of the reflection coefficient on the microwave wavelength of a circular waveguide with an anisotropic medium have been studied. 3D models of the propagation of the electromagnetic field of an anisotropic microwave circular waveguide were constructed for different values of the anisotropy coefficient of the medium. The influence of longitudinal anisotropy on the propagation constants and critical frequencies of a circular microwave waveguide is analyzed. It has been established that even in the case when the mode field configuration of the waveguide under study differs quite strongly from the mode field configuration of the reference waveguide, the single-wave approximation used gives values close to exact.