This research introduces a new technique for reduced-cost electromagnetic (EM)-driven multi-objective antenna optimization. Our approach employs artificial neural networks (ANNs) to build a surrogate model of antenna frequency characteristics, acting as a fast predictor providing multiple candidate Pareto-optimal solutions per iteration. The surrogate is refined within a machine-learning framework that leverages accumulated EM simulation data. Computational efficiency is enhanced by incorporating variable-fidelity EM simulations. Verification experiments underscrore competitive performance of our method, which requires only two hundred high-resolution EM analyses to complete the MO process. This represents 40% acceleration due to using variable-fidelity models and 90% speedup over traditional single-model surrogate-assisted methods. Our method is also shown competitive concerning design quality.