The Alderney Race has been identified as a future site for the development of tidal energy, due to its bidirectional strong current reaching 5 m/s during spring tides. This hydrodynamics is very difficult to measure by in-situ or remote sensing means. High-frequency coastal radars can provide a synoptic and near-real-time view of such a complex circulation, but the classical processing algorithms are not adapted to the extreme situation of strongly sheared currents. We propose an improved high-resolution direction-finding technique for the azimuthal processing of such radar data. It uses phased-array systems and combines the advantages of the usual beam-forming technique to eliminate many problems related to the distortion of Doppler spectra by extreme currents. The method is evaluated with a unique data set of radar measurements at two radar frequencies (13 and 24.5MHz) and three spatial resolutions (200, 750, and 1500 m). The radar-based surface currents are analyzed in the light of a high-resolution numerical model and also compared with in-situ measurements. While high azimuthal resolution can be achieved in this way, it is shown that the typical range resolutions of 750 and 1500 m are insufficient to account for the strong spatial variations of the surface current at some specific times and locations.