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Accurate and fast models are indispensable in contemporary antenna design. In this paper, we describe the low-cost antenna modeling methodology involving variable-fidelity electromagnetic (EM) simulations and co-Kriging. Our approach exploits sparsely sampled accurate (high-fidelity) EM data as well as densely sampled coarse-discretization (low-fidelity) EM simulations that are accommodated into one model using the co-Kriging technique. By using coarse-discretization simulations, the computational cost of creating the antenna model is greatly reduced compared to conventional approaches, where high-fidelity simulations are directly used to set up the model. At the same time, the modeling accuracy is not compromised. The proposed technique is demonstrated using three examples of antenna structures. Comparisons with conventional modeling based on high-fidelity data approximation, as well as applications for antenna design, are also discussed.