We discuss numerical models of ocean tidal currents, both depth-averaged (barotropic) and 3-D with stratification (baroclinic). Barotropic models applied to high latitudes have three difficulties: lack of high-quality satellite altimetry constraining the barotropic tide; the difficulty of predicting diurnal-band topographic vorticity waves, which carry much of the tidal kinetic energy along the shelf break; and critical latitude effects that significantly modify the structure of semidiurnal tides. We find that baroclinic models are needed in order to adequately map the tidal currents that affect sea ice. Upper-ocean tidal currents with baroclinicity included can greatly exceed the barotropic-only currents, while the smaller length scales of baroclinic waves relative to barotropic variability implies high spatial gradients of velocity and thus an increase in the shear, strain, divergence, and curl of the stress applied by the ocean to the sea-ice base. However, the need for high spatial resolution for resolving baroclinic tides implies that baroclinic tides can only be studied in focused regional models for the foreseeable future.