SUMMARYSpace mapping (SM) is one of the most popular techniques for creating computationally cheap and reasonably accurate surrogates of electromagnetic‐simulated microwave structures (so‐called fine models) using underlying coarse models, typically equivalent circuits. One of the drawbacks of SM is that although good modeling accuracy can be obtained using a limited number of training points, SM is not capable of efficiently utilizing larger amount of fine model information, even if it is available. In this paper, we consider various ways of enhancing SM surrogates by exploiting additional training data as well as two function approximation methodologies, kriging and co‐kriging. To our knowledge, it is the first application of co‐kriging for microwave circuit modeling. With three examples of microstrip filters, we present a comprehensive numerical study in which we compare the accuracy of the basic SM models as well as SM enhanced by kriging and co‐kriging. Direct kriging interpolation of fine model data is used as a reference. Copyright © 2012 John Wiley & Sons, Ltd.