Simultaneous EEG-fMRI allows multiparametric characterisation of brain function, in principle enabling a more complete understanding of brain responses; unfortunately the hostile MRI environment severely reduces EEG data quality. Simply eliminating data segments containing gross motion artefacts [MAs] (generated by movement of the EEG system and head in the MRI scanner's static magnetic field) was previously believed sufficient. However recently the importance of removal of all MAs has been highlighted and new methods developed. A systematic comparison of the ability to remove MAs and retain underlying neuronal activity using different methods of MA detection and post-processing algorithms is needed to guide the neuroscience community. Using a head phantom, we recorded MAs while simultaneously monitoring the motion using three different approaches: Reference Layer Artefact Subtraction (RLAS), Moire Phase Tracker (MPT) markers and Wire Loop Motion Sensors (WLMS). These EEG recordings were combined with EEG responses to simple visual tasks acquired on a subject outside the MRI environment. MAs were then corrected using the motion information collected with each of the methods combined with different analysis pipelines. All tested methods retained the neuronal signal. However, often the MA was not removed sufficiently to allow accurate detection of the underlying neuronal signal. We show that the MA is best corrected using the RLAS combined with post-processing using a multichannel, recursive least squares (M-RLS) algorithm. This method needs to be developed further to enable practical utility; thus, WLMS combined with M-RLS currently provides the best compromise between EEG data quality and practicalities of motion detection.