Numerical gate design typically makes use of high-dimensional parameterizations enabling sophisticated, highly expressive control pulses. Developing efficient experimental calibration methods for such gates is a long-standing challenge in quantum control, as on-device calibration requires the optimization of noisy experimental data over high-dimensional parameter spaces. To improve the efficiency of calibrations, we present a systematic method for reducing the dimensionality of the parameter space traversed in gate calibration, starting from an arbitrary high-dimensional pulse representation. We use this approach to design and calibrate an (X_{\pi/2}) gate robust against amplitude and detuning errors, as well as an (X_{\pi/2}) gate robust against coherent errors due to a spectator qubit.