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The optimum designs of microwave devices require highly accurate and efficient computer-aided-design systems. This paper describes a novel reduced-order model for the mode-matching technique, which is derived from the application of the Krylov subspace concept and of the singular-value-decomposition algorithm to the coupled integral equations solved by the mode-matching technique. The design example of a high performance 12-cavity Ka-band ridged-filter confirms the accuracy and the numerical efficiency of the proposed model. In particular, the presented method also enables to accurately control the metal losses of the devices.