This thesis investigates the impact of resonant overvoltages and their origin. Series and parallel resonances are present in any electrical grid. The frequency of which this resonance occurs is called resonance frequency. For parallel resonance, which is mainly being studied in this thesis, a high impedance peak can be found at the resonance frequency. This impedance peak in conjunction with a harmonic rich current cause a kind of temporary overvoltages called resonant overvoltages. The harmonic content of the current is high following a fault clearing in the grid, due to transformer saturation. The resonance frequency is heavily dependent on the amount of reactance present in the grid, which entail that a change in reactance causes a change in the resonance frequency. The electromagnetic transient tool PSCAD has been used to investigate resonant overvoltages following transformer energization caused by faults and switching in Stockholm. Secondly, a model was created of a grid connecting off-shore wind power to the mainland via long AC submarine transmission cables. These cables, having a high capacitance, lower the resonance frequency. Faults in this model were simulated to investigate the phenomenon of resonant overvoltages in such a grid. This was especially interesting due to Swedens planned expansion of wind power in the Baltic sea. While resonant overvoltages were found in Stockholm they were not deemed significant due to their low magnitude and longevity. However, severe resonant overvoltages were found in the off-shore wind farm model. The worst resonant overvoltages had a maximum amplitude of the 2nd order harmonic voltage of 130 kV which, while eventually damped, were significant for up to 50 periods. Lastly, the phenomenon of an increased resonance frequency during the saturation of a transformer was studied. The most severe resonant overvoltages occured in a model where the frequency scans showed a resonance frequency of 98 Hz. Indicating, caution needs to be had during EMT-studies of resonant overvoltages while choosing what resonance frequency to study.