Waves in some sophisticated waveguiding structures, filled with magnetised ferrite, are investigated. Anisotropic boundary conditions are supposed to be valid on some of the walls of the waveguides, whence the results allow, for instance, an analysis of ferrite-filled corrugated waveguides and microstrip lines with corrugated strips. For solving the related electromagnetic problems, a new approximate technique — averaging method — is used. The main idea is to average field inside a waveguide, assuming that the components tangential to the interfaces are locally quasistatic. The present technique can be used when one of the transversal dimensions of a waveguide is much smaller than the wavelength in that direction. The results could help to develop different devices, such as controlled phase-shifters and isolators.