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In this paper, a novel computer-aided design (CAD) tool of complex passive microwave devices in waveguide technology is proposed. Such a tool is based on a very efficient integral-equation analysis technique that provides a full-wave characterization of discontinuities between arbitrarily shaped waveguides defined by linear, circular, and/or elliptical arcs. For solving the modal analysis of such arbitrary waveguides, a modified version of the well-known boundary integral-resonant-mode expansion (BI-RME) method using the Nyström approach, instead of the traditional Galerkin version of the method of moments, is proposed, thus providing significant savings on computational costs and implementation complexity. The novel theoretical aspects of this Nyström approach, as well as their impact on the original BI-RME formulation, are fully described. Comparative benchmarks between this new technique and the classical BI-RME formulation using Galerkin are successfully presented for the full-wave analysis of frequently used irises (i.e., rectangular cross-shaped and circular multiridged) and for the CAD of complex waveguide components (such as rectangular waveguide filters considering mechanization effects and dual-mode circular waveguide filters with elliptical irises).