The North Sea is known for its marine activities, which need ocean data for safe operations. The ocean surface is described using the two-dimensional wave spectrum. This ocean wave spectrum can be estimated using wave buoys, wave models or remote sensing techniques. Wave buoys and numerical models are known to contain inaccuracies, which stresses the importance of other observation techniques. The solution of this thesis is using a remote sensing technique from Sentinel-1: Synthetic Aperture Radar. In total 11 case studies were analyzed in the North sea and 3 case studies in Portugal. Sentinel-1 SAR cross-spectra were verified and validated using wave buoy measurements and cross-spectra from simulated SAR images from OCEANSAR. In total, 6 North Sea case studies showed a positive result, where a swell peak was visible and the peak matched spectral data from wave buoys. Case studies from the Portuguese coast showed the best results, where SAR cross-spectra agreed well with buoy measurements. Further improvements include the removal of non-linear contribution from cross-spectra, mapping of wave buoy measurements on the quasi-linear swell spectrum and calculating the full Modulation Transfer Function. This thesis showed it is possible to measure low-frequency waves in the North Sea using Sentinel-1 Synthetic Aperture Radar. SAR images lead to a better understanding of the movements of swells and provide additional information for marine activities. A combination of wave buoy data, Sentinel-1 SAR data and OCEANSAR data showed measuring swell waves is possible with this state-of-the-art remote sensing technique.