Dual-satellite crossover data from the Jason-2 and Cryosat-2 altimeter missions are used in a novel approach to quantify stationary and non-stationary tides from time-lagged mean square sea-surface height (SSH) differences, computed for lags from 1 hour to 1440 hours (60 days). The approach is made feasible by removing independent estimates of the stationary tide and mesoscale SSH variance, which greatly reduces the sampling error of the SSH statistics. For the semi-diurnal tidal band the stationary tidal variance is approximately 0.73 cm^2, and the non-stationary variance is about 0.33 cm^2, or 30% of the total. The temporal correlation of the non-stationary tide is examined by complex demodulation and found to be oscillatory with first zero-crossing at 400 hours (17 days). Because a significant fraction of the time-variable mesoscale signal is resolved at time scales of roughly 150 h by the present constellation of satellite altimeters, the results suggest that it may be feasible to predict the non-stationary tide from modulations of the resolved mesoscale, thus enhancing the efficacy of tidal corrections for planned wide-swath altimeters such as the SWOT mission.