Cu(11n) surfaces vicinal to Cu(001) are characterized by (001) terraces separated by monoatomic steps. Growth of thin epitaxial magnetic films on such terraced substrates, e.g., Co/Cu(1 1 13), leads to unexpected magnetic anisotropy associated with the surface steps. This anisotropy remains largely unexplained, and is of potential technological importance. We have studied the anisotropy of fcc Co/Cu (1 1 13) films using in-situ magneto-optical Kerr effect (MOKE), and find an in-plane uniaxial anisotropy favoring magnetization parallel to the steps. The strength of this anisotropy decreases with increasing film thickness. In this paper we focus on the interpretation of this anisotropy in terms of the N\'eel model. The N\'eel anisotropy energy for such a film has the form ${\mathit{E}}_{\mathrm{film}}$= ${\mathit{E}}_{\mathrm{bulk}}$-2${\mathit{E}}_{\mathrm{surface}}$/t-2${\mathit{E}}_{\mathrm{step}}$/(td), where t and d are film thickness and terrace width, respectively. The last term includes contributions from sites at both the upper edge and inner corner of the step and makes the dominant contribution to the step-induced anisotropy. This model properly accounts for the preferred direction of magnetization parallel to the steps in Co/Cu(1 1 13). bcc Fe/W vicinal to (001) shows a preference for in-plane magnetization perpendicular to the steps for t2.5 monolayers. The N\'eel model also predicts this anisotropy for a bcc Fe film provided the magnetization lies in the film plane, not in the (001) plane.