Abstract: In a machining method for machining a curved workpiece surface (210) of a workpiece (200), a roll-embossing operation is carried out. At least one rolling element (180A, 180B, 180C) of a machining tool (100) is rolled here under a contact pressure against a section (198) to be machined of the curved workpiece surface. An external surface of the rolling element has a rough surface structure in at least one working section (190A, 190B, 190C) intended for rolling contact with the workpiece surface. The contact pressure is set in such a manner that, during the rolling, a rough roll-embossed structure is produced by local deformation of workpiece material without removing material in the machined region of the workpiece surface. The machining method can be used, for example, for machining the internal surface of a bore in a workpiece, in particular for roughening the workpiece surface for a subsequent coating.