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A method is presented for the efficient optimization of microwave filters and multiplexers designed from an ideal prototype. The method is based on the estimation of a rational function adjusted to a reduced number of samples of the microwave device response obtained either through electromagnetic analysis or measurements. From this rational function, a circuital network having the previously known topology of the microwave device is synthesized and compared to a circuital network with the desired response but including nonidealities. All of the process of analysis and model extraction can be seen as a model function that relates the physical parameters of the microwave device with the extracted circuital network parameters. Then, the error vector of the circuital parameters is used to generate a correction vector of the physical parameters through an estimation of the inverse of the Jacobian matrix of the complete model function. The Jacobian estimation is updated at each iteration of the optimization process with no need for additional evaluations of the model function. Two numerical examples of the proposed technique corresponding to the synthesis of a filter and a diplexer are presented, demonstrating the increased efficiency of the proposed technique with respect to direct electromagnetic optimization.