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Due to manufacturing and assembly variations, there are tolerances associated with the nominal dimensions of complex electromagnetic devices. A possible approach to take into account such tolerances in the early design phases is the “worst case tolerance analysis,” whose goal is to determine the effect of the largest variations on assembly dimensions on the product performance. On the other hand, when many tolerances must be considered, locating the worst case with combinatorial effects could get very time consuming, since performance assessment of such devices may require numerical field analysis. In this paper, a fast approach based on the performance sensitivity with respect to design parameters is presented, and applied to the tolerance analysis of nuclear magnetic resonance (NMR) magnets.