An analysis is made of contact damage in brittle coatings on metal substrates, using as a case study a dental porcelain coating of thickness between 0.1 and 1 mm fused onto a Pd alloy base, with spherical indenter of radii 2.38 and 3.98 mm. At large coating thicknesses (>300 um), the first damage takes the form of surface-initiated transverse cone cracks outside the contact. At small coating thicknesses (<300um), the first damage occurs as yield in the substrate, with attendant formation of subsurface transverse median cracks in the coating. At high loads and thin coatings, both forms of tansverse cracking occur, along with subsequent delamination of the ceramic/metal interface, signalling impending failure. Conditions for avoiding such transverse cracking are considered, in terms of minimum coating thicknesses and maximum sustainable contact loads. General implications concerning the design of brittle coating systems for optimum damage resistance are considred, but with special reference to dental crowns.