Simulation of electromagnetic fields in geophysical settings that include highly heterogeneous media and features varying at multiple spatial scales is computationally expensive. These settings often require very fine and large meshes to be discretized accurately. Large meshes lead to solve enormous linear systems of equations. In this talk, we introduce upscaling and multiscale finite volume methods that help to reduce the size of the system of equations to be solved. The performance of our methods is shown in the context of EM mineral exploration.