This work introduces the use of multivariate global sensitivity analysis for assessing the impact of uncertain electric machine design parameters on efficiency maps and profiles. Contrary to the common approach of applying variance-based (Sobol') sensitivity analysis elementwise, multivariate sensitivity analysis provides a single sensitivity index per parameter, thus allowing for a holistic estimation of parameter importance over the full efficiency map or profile. Its benefits are demonstrated on permanent magnet synchronous machine models of different fidelity. Computations based on Monte Carlo sampling and polynomial chaos expansions are compared in terms of computational cost. The sensitivity analysis results are subsequently used to simplify the models, by fixing non-influential parameters to their nominal values and allowing random variations only for influential parameters. Uncertainty estimates obtained with the full and reduced models confirm the validity of model simplification guided by multivariate sensitivity analysis.

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