Damping of ocean waves by sea ice is studied using spaceborne synthetic aperture radar (SAR) images of the marginal ice zone (MIZ) acquired by the European Remote sensing satellite ERS‐2. SAR imaging of waves damped by sea ice is analyzed theoretically. The impact of sea ice on the azimuthal cutoff is studied by simulation of the azimuthal SAR image autocorrelation function as well as the two‐ dimensional SAR image spectrum. Typical imaging artifacts like spiky wave crests and wave refraction seen on SAR scenes of the MIZ are reproduced by simulation. Sensitivity studies are performed using models for wind sea and swell systems. It is shown that the degradation of the azimuthal SAR image resolution is dominated by the orbital velocity variance of the waves, while the coherence time of the complex radar reflectivity has a minor impact. A first‐order analysis of wave damping observed on SAR scenes is carried out using a technique that was originally developed for wind estimation by Kerbaol et al. [1998]. The method does not require a priori information and is insensitive to real aperture modulation. The azimuthal SAR image cutoff wavelength is estimated and related to the orbital velocity variance of the sea surface by regression. The model is fitted on the basis of a global set of model ocean wave spectra. The technique is applied within the sea ice and in the open water in front of the ice boundary. On the basis of simple models for wind sea and swell, ocean wave attenuation rates are obtained from the observed orbital velocity decrease of waves entering the ice. The required wind information is derived from calibrated SAR data using the CMOD method. Two case studies showing examples from the Greenland and the Weddell Seas are given. It is shown that the estimated wave damping is consistent with damping parameters found in earlier field campaigns carried out in the Weddell Sea and the Bering Sea. An inversion technique providing estimates for the two‐dimensional wave spectra behind and in front of the ice boundary as well as a two‐dimensional filter function characterizing the sea ice impact is introduced. The technique is based on simultaneous inversion of the two‐dimensional image spectra in the open water and within the ice using a priori information from an ocean wave model. It is shown that the technique gives results consistent with the first‐order analysis based on the cutoff estimation.