Density functional supercell calculations of the Schottky barrier heights (SBH) of metal germanides and silicides on Si or Ge find that these vary with the facet, unlike those of elemental metals. In addition, silicides and germanides show a stronger dependence of their SBHs on the work function than those of elemental metals, as seen experimentally. Both effects are beyond the standard metal induced gap states model. NiSi2 is found to have a much lower SBH on n-Si(100) than on n-Si(111), as seen experimentally. It is shown how such results can be used to design lower SBH contacts for n-Ge, which are needed technologically. The SBHs of the better behaved Si/silicide interfaces can be used to benchmark the behavior of the less well behaved Ge-germanide interfaces for this purpose. The dependence of the SBH of epitaxial Pb-Si(111) on its reconstruction is also covered.