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A computationally efficient simulation-driven technique for design optimization of antennas is described. Our approach exploits a recently introduced shape-preserving response prediction (SPRP) technique as well as coarse-discretization EM simulations as the low-fidelity antenna model. SPRP allows us to estimate the outcome of the high-fidelity EM antenna simulation, e.g., its S11 versus frequency, using the properly selected set of so-called characteristic points of the low-fidelity model response. The SPRP-corrected model is then utilized to yield a prediction of the optimal antenna design. Shifting the optimization burden to the low-fidelity model and exploiting the reliability of the SPRP technique makes the design process cost efficient as demonstrated using two examples: dielectric resonator antenna and ultrawideband dipole antenna. In both cases, the optimal design is obtained at a cost corresponding to a few high-fidelity antenna simulations.