We present two independent, automated methods for estimating the horizontal misorientations of ocean bottom seismic sensors from their recorded data. The techniques measure the three-dimensional directions of particle motion of (1) P-waves and (2) Rayleigh waves of earthquake recordings. For P-waves, we used a principal component analysis to determine the directions of particle motions (polarisations) in multiple frequency passbands. Since P-wave polarisation may deviate from the direction of propagation due to seismic anisotropy and dipping discontinuities beneath stations, we further corrected for these deviations using a simple fit equation which yields sensor orientations of significantly increased accuracy. For Rayleigh waves, we evaluated the degree of elliptical polarisation in the vertical plane in the time and frequency domain. We apply both methods to 57 three-component broadband and wideband seismometers that were installed for 13 months on the ocean floor around La Réunion hotspot as part of the RHUM-RUM project (http://www.rhum-rum.net/). For P-wave polarisations we obtained misorientation estimates for 31 out of 44 functioning ocean-bottom seismometers (OBS), with an average uncertainty (95% confidence interval) of 11° per station. At 7 of these OBS, data coverage was sufficient to correct polarisation measurements for underlying seismic anisotropy and dipping discontinuities which improved the average orientation uncertainty to 6° per station. For Rayleigh-wave polarisations we obtained misorientation estimates for 40 out of 44 functioning OBS, with an average uncertainty (95% confidence interval) of 16° per station. Results obtained from the two methods are fully consistent within their respective error bars; the orientation angles differ on average by 3.1° and 3.7° for circular mean and median statistics, respectively. The good agreement between the two methods also makes them useful for reliably detecting possible misorientations of terrestrial seismic stations.