Simulation-based optimization has become an important design tool in microwave engineering. However, using electromagnetic (EM) solvers in the design process is a challenging task, primarily due to a high-computational cost of an accurate EM simulation. In this article, we present a review of EM-based design optimization techniques exploiting response-corrected physically based low-fidelity models. The surrogate models created through such a correction can be used to yield a reasonable approximation of the optimal design of the computationally expensive structure under consideration (high-fidelity model). Several approaches using this idea are reviewed including output space mapping, manifold mapping, adaptive response correction, and shape-preserving response prediction. A common feature of these methods is that they are easy to implement and computationally efficient. Application examples are provided.