We report a density functional theory study of N and NO passivation of surface dangling bonds at the Si-face of (0001) 4H-SiC. Results agree with many key experimental findings in nitrogen processed devices including: observed interface N coverage and characteristic changes in Dit. Dangling bonds at the SiC surface are fully passivated by 1/3 ML N or NO coverage. Upon passivation the surface is found to incur negligible strain and no reconstruction. Allowing atomic O to interact with the 1/3 ML N or NO passivated surface, we find oxygen prefers to incorporate into SiO2 rather than adsorb to the surface. This indicates the possibility of oxide deposition onto nitrogen passivated (0001) 4H-SiC surfaces.