In this paper, an explicit size reduction of a compact rat-race coupler implemented in a microstrip technology is considered. The coupler circuit features a simple topology with a densely arranged layout that exploits a combination of high- and low-impedance transmission line sections. All relevant dimensions of the structure are simultaneously optimized in order to explicitly reduce the coupler size while maintaining equal power split at the operating frequency of 1 ?GHz and sufficient bandwidth for return loss and isolation characteristics. Acceptable levels of electrical performance are ensured by using a penalty function approach. Two designs with footprints of 350 ?mm2 and 360 ?mm2 have been designed and experimentally validated. The latter structure is characterized by 27% bandwidth. For the sake of computational efficiency, surrogate-based optimization principles are utilized. In particular, we employ an iterative construction and re-optimization of the surrogate model involving a suitably corrected low-fidelity representation of the coupler structure. This permits rapid optimization at the cost corresponding to a handful of evaluations of the high-fidelity coupler model.