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A simulation-driven optimization framework for computationally efficient design of ultrawideband (UWB) antennas is presented. Our approach exploits coarsely-discretized electromagnetic (EM) simulations as a low-fidelity model of the antenna under consideration. This low-fidelity model is used as a prediction tool to find an approximate optimum design. The discrepancy between the low- and the high-fidelity models is accounted for by appropriate modifications of the design requirements. Efficiency of the presented technique is demonstrated through the design of an UWB monopole and an antipodal Vivaldi antenna.