We sputtered Pt/Co and Pd/Co multilayers on single-crystal, c-axis-oriented platelets of ZnO. The Pt/Co multilayers grew epitaxially with Pt/Co(111)ZnO(001) and Pt/Co[110BAR]ZnO[110BAR], as characterized by high resolution electron microscopy of the film cross-section. Both multilayers had a very large perpendicular magnetic anisotropy energy compared with identical films grown on glass substrates. K(eff) was 2.4 x 10(7) erg cm-3-Co (2.4 MJ m-3-Co) for Pt/Co and 2.9 x 10(7) erg cm-3-Co (2.9 MJ m-3-Co) for Pd/Co multilayers grown on ZnO, comparable with multilayers grown by molecular beam epitaxy (MBE) and four and three times larger respectively than identical multilayers grown on glass substrates. However, coercivities were smaller, H(c) = 1.1 kOe for Pt/Co and H(c) = 2.5 kOe for Pd/Co, than those reported for highly textured and crystalline multilayers MBE grown on textured metal underlayers, suggesting that larger coercivities are predominantly caused by growth-induced microstructural features and not by a larger anisotropy energy.