Vulnerability assessments of the risk posed by geomagnetically induced currents (GICs) to power transmission grids benefit from accurate knowledge of the geomagnetic field variations at each node of the grid, the Earth's geoelectrical structures beneath them, and the topology and relative resistances of the grid elements in the precise instant of a storm. The results of previous analyses on the threat posed by GICs to the Spanish 400 kV grid are improved in this study by resorting to different strategies to progress in the three aspects identified above. First, although at midlatitude regions the source fields are rather uniform, we have investigated the effect of their spatial changes by interpolating the field from the records of several close observatories with different techniques. Second, we have performed a magnetotelluric (MT) sounding in the vicinity of one of the transformers where GICs are measured to determine the geoelectrical structure of the Earth, and we have identified the importance of estimating the MT impedance tensor when predicting GIC, especially where the effect of lateral heterogeneities is important. Finally, a sensitivity analysis to network changes has allowed us to assess the reliability of both the information about the network topology and resistances, and the assumptions made when all the details or the network status are not available. In our case, the most essential issue to improve the coincidence between model predictions and actual observations came from the use of realistic geoelectric information involving local MT measurements.