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We introduce a new waveguide port algorithm for transient FEM computations. The waveguide port algorithm is suitable for homogeneous waveguides of arbitrary cross section as well as similar problems in, e.g. acoustics. Assuming that a sufficient number of waveguide modes is used, the suggested algorithm does not give any reflection from the waveguide port. This result holds for all frequencies supported by the FEM discretization. We demonstrate the new waveguide port algorithm by using it in conjunction with the stable FEM-FDTD hybrid (Rylander, T. and Bondeson, A., Comput. Phys. Comm., vol.125, p.75-82, 2000; J. Comput. Phys., vol.179, p.426-38, 2002) for the computation of the scattering parameter of a patch antenna fed by a coaxial cable. The coaxial cable and a small volume around the feed are discretized by the FEM and the remaining large volume (including the major part of the substrate) is discretized by the FDTD scheme.