Seafloor massive sulphides (SMSs) are regarded as a potential future resource to satisfy the growing global demand of metals including copper, zinc and gold. Aside from mining and retrieving profitable amounts of massive sulphides from the seafloor, the present challenge is to detect and delineate significant SMS accumulations, which are generally located near mid-ocean ridges and along submarine volcanic arc and backarc spreading centres. Currently, several geophysical technologies are being developed to detect and quantify SMS occurrences that often exhibit measurable contrasts in their physical parameters compared to the surrounding host rock. Here, we use a short, fixed-offset controlled source electromagnetic (CSEM) system and a coincident-loop transient electromagnetic (TEM) system, which in theory allow the detection of SMS in the shallow seafloor due to a significant electrical conductivity contrast to their surroundings. In 2016, CSEM and TEM experiments were carried out at several locations near the TransAtlantic Geotraverse hydrothermal field to investigate shallow occurrences of massive sulphides below the seafloor. Measurements were conducted in an area that contains distinct SMS sites located several kilometres off-axis from the Mid-Atlantic ridge, some of which are still connected to hydrothermal activity and others where hydrothermal activity has ceased. Based on the quality of the acquired data, both experiments were operationally successful. However, the data analysis indicates bias caused by three-dimensional (3D) effects of the rough bathymetry in the study area and, thus, data interpretation remains challenging. Therefore, we study the influence of 3D bathymetry for marine CSEM and TEM experiments, focusing on shallow 3D conductors located beneath mound-like structures. We analyse synthetic inversion models for attributes associated with 3D distortions of CSEM and TEM data that are not sufficiently accounted for in conventional 1D (TEM) and 2D (CSEM) interpretation schemes. Before an adequate quantification of SMS in the region is feasible, these 3D effects need to be studied to avoid over/underestimation of SMS using the acquired EM data. The sensitivity of CSEM and TEM to bathymetry is investigated by means of 3D forward modelling, followed by 1D (TEM) and 2D (CSEM) inversion of the synthetic data using realistic error conditions. Subsequently, inversion models of the synthetic 3D data are analysed and compared to models derived from the measured data to illustrate that 3D distortions are evident in the recorded data sets.