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Gaussian process (GP) regression, a structured supervised learning alternative to neural networks for the fast modeling of antenna characteristics, is applied to modeling S11 and gain against frequency of a dual-band microstrip patch antenna with separate tuning strips on a three-layer substrate. Since the two frequency bands of the antenna are relatively narrow, the function underlying the variation of S11 with four geometry variables and frequency is challenging to map. Predictions using large test data sets yielded results of an accuracy comparable to the target moment-method-based full-wave simulations; highly favourable mean square errors were obtained. The GP methodology has various inherent advantages that include ease of implementation and the need to learn only a handful of (hyper) parameters.