Embodiments of an apparatus, and a method for crimping expandable stents or prosthetic valves having a radially expandable and compressible annular body and one or more protruding anchors extending from the body using the apparatus, where the apparatus comprise a housing, a plurality of circumferentially arranged nesting jaws, and an actuator configured to move the jaws radially inwardly to reduce the size of the crimping aperture, thereby radially compressing the annular body of the prosthetic valve or stent. In particular embodiments, a selected set of the jaws, each having a front side and a recessed portion in its front side adjacent to its inner end. The recessed portions of the selected jaws collectively are sized and shaped to receive the one or more anchors of the prosthetic valve when the annular body is positioned within the crimping aperture.