Our knowledge of magma dynamics would be improved if geophysical data could be used to infer rheological constraints in melt-bearing zones. Geophysical images of the Earth's interior provide frozen snapshots of a dynamical system. However, knowledge of a rheological parameter such as viscosity would constrain the time-dependent dynamics of melt bearing zones. We propose a model that relates melt viscosity to electrical conductivity for naturally occurring melt compositions (including H2O) and temperature. Based on laboratory measurements of melt conductivity and viscosity, our model provides a rheological dimension to the interpretation of electromagnetic anomalies caused by melt and partially molten rocks (melt fraction ~ >0.7).