Synthetic Aperture Magnetometry (SAM) is a beamformer approach for the localisation of neuronal activity from EEG/MEG data. SAM estimates the optimum orientation of each source in a predefined source space by a nonlinear search for the orientation that maximises the beamformer output. However, MEG is most sensitive to cortical sources and these sources are generally oriented perpendicular to the surface. The reconstructed neuronal activity can therefore reasonably be constrained to the cortical surface, orientated perpendicular to it, therefore removing the search for the optimum orientation for the computation of the beamformer weights. This paper sets out to compare the performance of a constrained and unconstrained beamformer (SAM), with respect to the localisation accuracy of the source reconstructions and the spatial resolution. Fifty sources were randomly placed on a cortical surface estimated from an MRI, and we simulated data over a range of different signal-to-noise ratios (SNRs) for each source. These datasets were analysed using both an unconstrained beamformer (SAM) and a constrained beamformer (with the sources orientated perpendicular to the cortical surface). The influence of errors in the estimation of the surface location and surface normals on the performance of the constrained beamformer, representing MEG/MRI coregistration and segmentation errors, were also examined. The spatial resolution of the beamformer improves, typically by a factor of four by applying anatomical constraints, and the localisation accuracy improves marginally. However, the advantage in spatial resolution disappears when errors are introduced into the orientation and location constraints, and, moreover, the localisation accuracy of the inaccurately constrained beamformer degrades rapidly. We conclude that the use of anatomical constraints is only advantageous if the MEG/MRI coregistration error is smaller than 2 mm and the error in the estimation of the cortical surface orientation is smaller than 10 degrees.