We present a new method for the analysis of smoothly varying tapers, transitions and filters in rectangular waveguides. With this aim, we apply a Hierarchical Model (HiMod) reduction to the vector Helmholtz equation. We exploit a suitable coordinate transformation and, successively, we use the waveguide modes as a basis for the HiMod expansion. We show that accurate results can be obtained with an impressive speed-up factor when compared with standard commercial codes based on a three-dimensional finite element discretization.