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A robust new algorithm for electromagnetic (EM) optimization of microwave circuits is presented. The algorithm (TRASM) integrates a trust region methodology with the aggressive space mapping (ASM). The trust region ensures that each iteration results in improved alignment between the coarse and fine models needed to execute ASM. The parameter extraction step is a crucial part of the ASM technique. The nonuniqueness of this step may result in the divergence of the technique. To improve the uniqueness of the extraction phase, we developed a recursive multipoint parameter extraction. This suggested step exploits all the available EM simulations for improving the uniqueness of parameter extraction. The new algorithm was successfully used to design a number of microwave circuits. Examples include the EM optimization of a double-folded stub filter and of a high-temperature superconducting (HTS) filter …