Solution of the Electro-Magnetic Source Imaging (EMSI) problem requires an accurate representation of the head using a numerical model. Some of the errors in source estimation are due to the differences between this model and the actual head. This study investigates the effects of conductivity perturbations, that is, changing the conductivity of a small region by a small amount, on the EEG and MEG measurements. By computing the change in measurements for perturbations throughout the volume, it is possible to obtain a spatial distribution of sensitivity. Using this information, it is possible, for a given source configuration, to identify the regions to which a measurement is most sensitive. In this work, two mathematical expressions for efficient computation of the sensitivity distribution are presented. The formulation is implemented for a numerical head model using the finite element method (FEM). 3D sensitivity distributions are computed and analyzed for selected dipoles and sensors. It was observed that the voltage measurements are sensitive to the skull, the regions near the dipole and the electrodes. The magnetic field measurements are mostly sensitive to regions near the dipole. It could also be possible to use the computed sensitivity matrices to estimate or update the conductivity of the tissues from EEG and MEG measurements.