Spectral and diffraction characteristics of cylindrical resonators loaded on various cylindrical or coaxial waveguides are investigated. The partial inversion method is used to solve this class of problems and to develop the corresponding numerical algorithms. It is demonstrated that the observed effects of total resonant reflection and transmission are caused by the excitation of induced oscillations close to the eigenmodes of the problem. The spectral domain solution enables us to predict the effects of complete mode transformation by open waveguide resonators (OWR). Detailed investigation of coupled eigenmodes in OWRs has determined that the phenomenon is due to the Morse critical points (MCP) of the characteristic determinant of the boundary value problem.