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Convergence is a well-known issue for standard space-mapping optimization algorithms. It is heavily dependent on the choice of coarse model, as well as the space-mapping transformations employed in the optimization process. One possible convergence safeguard is the trust region approach where a surrogate model is optimized in a restricted neighborhood of the current iteration point. In this paper, we demonstrate that although formal conditions for applying trust regions are not strictly satisfied for space-mapping surrogate models, the approach improves the overall performance of the space-mapping optimization process. Further improvement can be realized when approximate fine model Jacobian information is exploited in the construction of the space-mapping surrogate. A comprehensive numerical comparison between standard and trust-region-enhanced space mapping is provided using several examples of microwave design problems.