A prosthesis (10) for a heart valve (e.g., the mitral valve) is generally C-shaped in plan view. Points at the top (12) and bottom (14) of the C lie in a plan view plane. The back (30) of the C rises above the plan view plane between the top and bottom points. Free end portions (42, 44) of the C may also rise above the plan view plane. The prosthesis is accordingly saddle-shaped. The back of the C may have an indentation that extends toward the open side of the C. In use as a mitral valve prosthesis the top and bottom of the C are respectively adjacent the commissures of the valve, and the back of the C is adjacent the posterior section of the valve. The prosthesis may be rigid or semi-rigid.