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The authors present efficient space mapping (SM) modelling of microwave devices where they assume a tight limit on the number of high-fidelity electromagnetic (EM) simulations available to set up a suitable model. The authors' method exploits a two-stage procedure. In the first stage, the standard SM surrogate is enhanced by a functional approximation layer using coarse-mesh EM simulation data. In the second stage, this surrogate is updated through space-mapping-based matching to high-fidelity EM simulation responses at a limited number of base locations (designs). The first stage normally uses a physically based coarse model, but in some cases direct approximation of the coarse-mesh EM simulation data is sufficient. The authors demonstrate that their proposed approach improves modelling accuracy in comparison with standard SM, and no extra fine model evaluations are required to set up the model. Applications to parametric design optimisation are discussed.