The emergency bearing for a rotary machine having magnetic bearings comprises an emergency landing device including an intermediate element (9) having a large contact area with a stator element (10), the intermediate element (9) being interposed between a bearing member (1, 2, 3) and the stator element (10) fixed to the stator (15) with radial clearance (11, 13) relative to said stator element (10). A damper element (13) acting in the radial direction is interposed between the intermediate element (9) and the stator element (10), and a contact element (14) having very low friction is implemented between the intermediate element (9) and the stator element (10) to reduce friction during rotary movements between these two elements.