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There is a significant need for efficient and accurate macromodels of components during the design of microwave circuits. Increased integration levels in microwave devices and higher signal speeds have produced the need to include effects previously neglected during circuit simulations. Accurate prediction of these effects involve solution of large systems of equations, the direct simulation of which is prohibitively CPU expensive. In this paper, an algorithm is proposed to form passive parametrized macromodels of large linear networks that match the characteristics of the original network in time, as well as other design parameters of the circuit. A novel feature of the algorithm is the ability to incorporate a set of design parameters within the reduced model. The size of the reduced models obtained using the proposed algorithm were less than 5% when compared to the original circuit. A speedup of an order of magnitude was observed for typical high-speed transmission-line networks. The algorithm is general and can be applied to other disciplines such as thermal analysis.