Determining the anatomical source of brain activity non-invasively measured from EEG or MEG sensors is challenging. In order to simplify the source localization problem, many techniques introduce the assumption that current sources lie on the cortical surface. Another common assumption is that this current flow is orthogonal to the cortical surface, thereby approximating the orientation of cortical columns. However, normal vectors computed from a single cortical surface may not be the best approximation to the orientation of cortical columns. We compared four different approaches for estimating dipole vector orientation, both in simulations and visual and motor evoked MEG responses. We show that methods based on establishing correspondences between white matter and pial cortical surfaces dramatically outperform methods based on the geometry of a single cortical surface in fitting evoked visual and motor responses. These methods can be easily implemented and adopted in most M/EEG analysis pipelines, with the potential to significantly improve source localization of evoked responses.Using vectors orthogonal to the cortical surface may not be the best approximation to the orientation of cortical columns. Cortical folding patterns may result in curved cortical columns, and therefore their orientation with respect to the cortical surface could be different along the gray / white matter (white matter surface) and CSF / gray matter (pial surface) boundaries. In the past, however, the contribution of inaccuracies in dipole orientation constraints to source localization error has likely been insignificant in the face of within-session participant movement, co-registration error, and the relatively low resolution of cortical surface reconstructions. However, the recent development of techniques for high precision MEG (Bonaiuto et al., 2018b, 2018aMeyer et al., 2017;Troebinger et al., 2014bTroebinger et al., , 2014a allow us to compare competing current-flow orientation models in more detail.Here, we set out to determine the best way to estimate the orientation of source dipoles based on MRIderived cortical surfaces. We tested four different methods for computing dipole orientations: 1) downsampled surface normals, 2) original surface normals, 3) link vectors, and 4) variational vector fields.