Anchoring or docking devices configured to be positioned at a native valve of a human heart and to provide structural support for docking a prosthetic valve therein. The docking devices can have coiled structures that define an inner space in which the prosthetic valve can be held. The docking devices can have enlarged end regions with circular or non-circular shapes, for example, to facilitate implantation of the docking device or to better hold the docking device in position once deployed. The docking devices can be laser-cut tubes with locking wires to assist in better maintaining a shape of the docking device. The docking devices can include various features to promote friction, such as frictional cover layers. Such docking devices can have ends configured to more securely attach the cover layers to cores of the docking devices.
