A very efficient technique for the full-wave analysis and design of complex passive waveguide filters, including rectangular cavities with metallic cylindrical posts and coaxial excitation, is presented. This novel technique provides the wideband generalized admittance matrix representation of the whole structure in the form of pole expansions, thus extracting the most expensive computations from the frequency loop. For this purpose, the structure is properly segmented into its key building blocks, all of them characterized in terms of wideband admittance matrices. Then, an efficient iterative algorithm for combining these matrices, and finally providing the wideband generalized admittance matrix of the complete structure, is followed. In order to validate the accuracy and efficiency of this full-wave modal technique, four different waveguide filters have been considered. In particular, the design of a compact four-pole in-line filter with tuning screws and of an evanescent-mode filter, both operating in the X-band and including a standard (vertical) coaxial excitation, are first presented. Finally, two C-band six-resonator comb-line filters, one of them with a cross-coupling configuration, and both excited with a collinear end-launcher transition based on a disc-ended coaxial, are also designed. Numerical data from a commercial software, as well as measurements of a manufactured prototype, are included for verification purposes.