Self-retaining shim for use with a contoured machining template

Self-retaining shim apparatus and methods for providing an offset surface for supporting a template above a contoured workpiece such as the frame of an aircraft are disclosed. In one embodiment, an apparatus includes a shim portion of substantially uniform thickness, and one or more biasing members secured to the distal end thereof and extending toward the proximal end. A work piece is positioned between the biasing member and shim portion such that the biasing members are elastically deformed, resulting in a restoring force exerted on the workpiece serving to retain the shim in engagement with the workpiece. Contact pads secure to the free ends of the biasing members and have a contact portion offset from the free end. The contact portion is rounded to facilitate mounting and retention of the self-retaining shim.