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We apply a fine-integral formulation to the hybrid mode-matching/FEM Technique for the analysis of discontinuities with waveguides of arbitrary cross-section. The line-integral formulation is used instead of standard surface integrals, not only for the evaluation of coupling integrals but also for normalization integrals computation. In this way a noticeable advantage is gained in terms of numerical efficiency, particularly when accurate solutions are sought for. Numerical examples validate the proposed approach.