With the aim of understanding electrochemical scanning tunnel microscopy experiments in an aqueous environment, we investigate electron transport through ice in the coherent limit. This is done by using the nonequilibrium Greens functions method, implemented within density functional theory, in the self-interaction corrected local density approximation. In particular, we explore different ice structures and different Au electrode surface orientations. By comparing the decay coefficient for different thicknesses to the ice complex band structure, we find that the electron transport occurs via tunneling with almost one-dimensional character. The slow decay of the current with the ice thickness is largely due to the small effective mass of the conduction electrons. Furthermore, we find that the calculated tunneling decay coefficients at the Fermi energy are not sensitive to the structural details of the junctions and are at the upper end of the experimental range for liquid water. This suggests that linear response transport measurements are not capable of distinguishing between different ordered ice structures. However, we also demonstrate that a finite bias measurement may be capable of sorting polar from nonpolar interfaces due to the asymmetry of the current-voltage curves for polar interfaces. © 2012 American Chemical Society.