A combination of 1D and 3D forward and inverse solutions is used to quantify the sensitivity and resolution of conventional controlled source electromagnetic (CSEM) data collected using a horizontal electric dipole source to transverse electric anisotropy located in a deep-water exploration reservoir target. Because strongly anisotropic shale layers have a vertical resistivity that can be comparable to many reservoirs, we examined how CSEM can discriminate confounding shale layers through their characteristically lower horizontal resistivity. Forward modeling indicated that the sensitivity to reservoir level anisotropy is very low compared with the sensitivity to isotropic reservoirs, especially when the reservoir is deeper than about 2 km below the seabed. However, for 1D models where the number of inversion parameters can be fixed to be only a few layers, both vertical and horizontal resistivity of the reservoir can be well resolved using a stochastic inversion. We found that the resolution of horizontal resistivity increases as the horizontal resistivity decreases. This effect is explained by the presence of strong horizontal current density in anisotropic layers with low horizontal resistivity. Conversely, when the reservoir has a vertical to horizontal resistivity ratio of about 10 or less, the current density is vertically polarized and hence has little sensitivity to the horizontal resistivity. Resistivity anisotropy estimates from 3D inversion for 3D targets suggest that resolution of reservoir level anisotropy for 3D targets will require good a priori knowledge of the background sediment conductivity and structural boundaries.