The retrieval of quantitative information on ocean waves from SAR images is a challenging problem because of the nonlinearities of the imaging mechanism, the presence of speckle noise, and the directional ambiguities associated with the interpretation of a SAR image as a single snapshot in time. We present a new methodology that overcomes some of these problems by utilizing spotlight-mode data from TerraSAR-X and COSMO-SkyMed in combination with advanced subaperture processing. We are able to derive short time series of subaperture images, which show propagation directions and speeds of moving patterns. Then we can use Fourier analysis and a dispersion relation filter to separate actual ocean wave signatures from other contributions. This process is phase-preserving and lets us reconstruct short "videos" of the spatio-temporal evolution of the extracted wave signatures, which are easier to invert into surface slope and elevation fields than conventional SAR images.