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This paper presents an efficient method for fast wideband eigenmode analysis of waveguide structures. The proposed algorithm uses a multidimensional subspace method based on modified perturbation theory and singular-value decomposition to perform model-order reduction directly on the finite element eigenvalue equations. This procedure generates parametric reduced order models that are valid over the desired parameter range without the need to redo the reduction when design parameters are changed. Numerical examples of a dielectric loaded rectangular waveguide and a microstrip line are provided illustrating the validity of the proposed method.