Methods of implanting docking devices for prosthetic valves at a native heart valve include positioning a distal end of a delivery catheter into a first chamber of a heart, advancing a tubular body of a docking device from within the delivery catheter so that the distal end of the tubular body is advanced between native valve leaflets and positioned in a second chamber of the heart. The methods further include inserting a coil into a lumen of the docking device so that the tubular body adopts a configuration, releasing a proximal end of the docking device in the first chamber, inserting a replacement valve in an inner space of the docking device, and radially expanding the replacement valve until there is a retention force between the replacement valve and the docking device to hold the replacement valve in a stable position in the native valve.