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A hybrid mode matching/finite element method (FEM) for the analysis of waveguide discontinuities is presented. The method combines the computational efficiency of the modal analysis with the versatility and flexibility of the FEM, and enables us to accurately model geometries where a modal expansion is not available. Moreover, the use of Whitney's edge element within the FEM region allows us to overcome the problem of the spurious solutions arising in nodal FEM. Numerical results that illustrate the accuracy of the method are presented.