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In this paper, we present two contributions. First, we develop a computationally efficient technique for the full-wave characterization of inhomogeneously dielectric-filled cavities connected to inhomogeneously dielectric-loaded waveguides. This method is based on the expansion of the electromagnetic field within the cavity in terms of their solenoidal and irrotational modes. The presented formulation allows the treatment of hybrid modes in the waveguide ports, where the definition of a characteristic modal impedance or admittance is not possible. The multimode scattering matrix of the structure is computed throughout an efficient implementation of the orthonormal-basis method for the calculation of the cavity modes. Secondly, we have employed the present technique for the analysis and design of nonradiative dielectric (NRD) guide components and discontinuities. Moreover, the application of the bi-orthonormal-basis method for the calculation of the full-spectrum of NRD guides is demonstrated as being a very efficient approach for the rigorous treatment of such guides. Next, an efficient computer-aided design tool has been developed for the analysis of complex NRD-guide circuits. We have compared our simulations with theoretical and experimental results available in the technical literature, fully validating our software. This code has been employed for the specific analysis of a linear continuous taper to match two NRD guides with different widths, demonstrating a considerable reduction of the return losses over a wide frequency band. Finally, stopband and bandpass NRD-guide filters based on an electromagnetic-bandgap concept are presented.