Solar magnetic fields are usually extrapolated into the corona starting from photospheric mag-netic measurements that can suffer from significant uncertainties caused by the presence of unresolved fine structures due to a limited spatial resolution and by the limited polarimet-ric accuracy and spectral resolution. We investigate how these inaccuracies in the measured photospheric magnetic field vector influence the accuracy of the extrapolated coronal mag-netic field. We compare non-linear force-free coronal magnetic field extrapolations from a 3-D radiation MHD simulation snapshot with corresponding extrapolations from synthetic vector magnetograms. The synthetic magnetograms contain instrumental effects such as noise, limited spatial and spectral resolution and the effect of employing a filter instrument. The parameters are chosen in particular to mimic the effects of the Hinode/SOT and the future Solar Orbiter PHI instruments, respectively. We discuss, how photospheric structures, which are inherent in the MHD snapshot, but not resolved in the photospheric magnetic field measurements, influence the quality of the computed coronal magnetic field model.