Some neurosurgery procedures require precise information on the region of interest, and a quantitative control of the overall uncertainty. Such procedures often rely on image registration, which is an essential step in many of these workflows. However, the problem of registration error estimation (REE) remains a challenge, due to its lack of ground-truth. In this work, we establish different criteria to evaluate REE methods and we propose a regression U-Net, a supervised convolutional neural network approach, that is able to compute the REE for the case of deformable brain MRI mono-modal registration. The model is trained and tested separately on four modalities. The best result is for T1 images, with a root mean square deviation (RMSD) on the test set of 0.17 mm for images with 1 mm \(^3\) isotropic voxels. We also tested the model generalization and transfer learning capabilities on a separate MRI data set with two modalities. For the T1 images, the direct inference has a RMSD of 0.62 mm and the transfer learning method leads to a RMSD of 0.19 mm, also for volumes of 1 mm \(^3\) voxel size. These results demonstrate the feasibility of our approach and the possible use of a U-Net based model for REE in brain MRI registration. The proposed methods enable a better quantitative control of procedure uncertainty in neurosurgeries and open the way to closed loop robotic control in these procedures.