We present transport calculations with the Ultra-relativistic Quantum Molecular Dynamics approach (UrQMD) for dilepton spectra at SIS energies and simulations for NA60 within a coarse-graining approach. While the transport model obtains a good agreement with experiment for elementary reactions, in heavy-ion collisions an excess in the invariant mass spectra is observed which cannot be described by the model. As the pure transport calculations do not include explicit in-medium effects and are limited to hadronic degrees of freedom, we present an alternative approach that uses coarse-grained output from transport calculations to determine thermal dilepton emission rates. For this we apply the medium-modified ρ spectral function by Eletsky et al. In a first exemplary comparison to data from the NA60 experiment we find that the coarse-graining approach gives reasonable results.