Electrochemical polishing of Si- and C-face p-type 4H SiC has been performed. Polishing the Si face leads to a smoother surface compared to the C face within the range of etching conditions studied. However, the results of additional experiments on C-face samples indicate that polishing a lower doped p-type material leads to improved surface quality for this face. Differences in polishing on the two faces are interpreted in terms of preferred electrochemical etching directions in SiC. Etching conditions such as HF concentration, doping, and etching current density were varied to obtain optimized values. Current-voltage plots (voltammograms) show a maximum electrochemical current density for the process. The polishing should be performed at a constant current density near this peak value to obtain both a smooth surface and a rapid rate of removal of material. In contrast to electrochemical polishing of silicon, we suggest that the applied current should match the rate at which the electrolyte can supply ions for reaction to obtain the smoothest surface required for microelectromechanical system device fabrication. Based on the experiments, we propose that, to obtain the smoothest SiC surface using electrochemical polishing, etching should be performed on Si-face p-type 4H SiC in dilute HF solution at the optimum current density determined by the current-voltage measurements.