Altimeter data from the CryoSat-2 mission have been used to map ocean tides in the Weddell Sea and on the Larsen and Filchner-Ronne Ice Shelves. The orbit of CryoSat-2 was not designed to observe tides, but usefully accurate estimates of the M2, S2, K1, and O1 tides have been obtained by spatially-coupled harmonic analysis which locally represents the tidal elevation as the product of temporal tidal harmonics with spatial basis functions. Analysis of the CryoSat-2 orbit from the point of view of space- and time- aliasing and resolution will be presented, as will issues related to the mean surface and treatment of off-nadir returns from SARin mode data. Comparison of published GPS-based estimates with the empirical CryoSat-2 tide maps finds agreement comparable to that of previous data assimilative tide models. The amplitudes of the annual and semiannual cycles on the ice shelf, but not open-ocean, are much larger than observed by GPS. It is hypothesized that the apparent cycle at these periods is related to snow depth or radar penetration of snow and ice, rather than ice sheet elevation level per se. The purpose of obtaining new tide estimates from CryoSat-2 is to assimilate them into an inverse model for the shape and depth of the under-ice cavities adjoining the Weddell Sea, and the status of this effort will also be reported.