By employing state-of-the-art automated design and optimization techniques from the field of evolutionary computation, engineers are able to discover electrical machine designs that are highly competitive with respect to several objectives like efficiency, material costs, torque ripple and others. Apart from being Pareto-optimal, a good electrical machine design must also be quite robust, i.e., it must not be sensitive with regard to its design parameters as this would severely increase manufacturing costs or make the physical machine exhibit characteristics that are very different from those of its computer simulation model. Even when using a modern parallel/distributed computing environment, carrying out a (global) tolerance analysis of an electrical machine design is extremely challenging because of the number of evaluations that must be performed and because each evaluation requires very time-intensive non-linear finite element (FE) simulations. In the present research, we describe how global surrogate models (ensembles of fast-to-train artificial neural networks) that are created in order to speed-up the multi-objective evolutionary search can be easily reused to perform a fast tolerance analysis of the optimized designs. Using two industrial optimization scenarios, we show that the surrogate-based approach can offer very valuable insights regarding the local and global sensitivities of the considered objectives at a fraction of the computational cost required by a FE-based strategy. Encouraged by the good performance on individual designs, we also used the surrogate approach to track the average sensitivity of the Pareto front during the entire optimization procedure. Our results indicate that there is no generalized increase of sensitivity during the runs, i.e., the used evolutionary algorithms do not enter a stage where they discover electrical drive designs that trade robustness for quality.