We study the equilibrium configuration of a nematic liquid crystal bounded by a rough surface. If ξ and η are, respectively, the nematic coherence length and the characteristic wavelength of the roughness, we show that in both limiting cases ξ ≪ η and η ≪ ξ the wrinkling of the surface induces a nontrivial structure in the equilibrium solution which may be interpreted in terms of an effective weak anchoring potential. We also determine how the effective surface extrapolation length is related to the microscopic anchoring parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)