We analyze the electromagnetic field (EMF) of a small bunch that moves uniformly in a circular metal waveguide and crosses the boundary between two areas: a vacuum area and an area loaded with an anisotropic homogeneous nondispersive dielectric characterized by a diagonal permittivity tensor. Two cases are studied in detail: the bunch flies from a vacuum into the dielectric and, inversely, from the dielectric into a vacuum. In the second case, so-called Cherenkov-transition radiation (CTR) can be generated in the vacuum area of the waveguide. Exact expressions for the EMF components are obtained and investigated. A comparison between the present problems and the analogous problems in the case of an isotropic dielectric is performed. We discuss some benefits occurring from using the anisotropic dielectric. For example, anisotropic dielectric allows more efficient generation of radiation compared to the isotropic dielectric for the same bunch and geometry parameters.