The global sensitivity analysis of electromagnetic nondestructive evaluation (NDE) by means of Sobol' indices are considered in this work. To reduce the computational burden, a sparse grid surrogate model is used. The latter can simply replace the true simulator to some extent, but it can also be used to numerically evaluate the integrals defining the Sobol' indices. In most of the NDE setups, the output is not a scalar quantity but functional data (e.g., a surface scan); a method is presented to take this into account. The sparse grid based sensitivity analysis is compared to classical techniques via examples drawn from electromagnetic NDE.