Delivery systems with tethers for prosthetic heart valve devices and associated methods are disclosed herein. A delivery system configured in accordance with embodiments of the present technology can include, for example, an elongated catheter body, a capsule carried by the elongated catheter body and carrying a prosthetic heart valve device, and a cinching member slidably disposed within the capsule. The delivery system can further include a plurality of tether elements coupled to the prosthetic device and extending through the cinching member and the catheter body. Retraction of the tether elements can urge at least a portion of the prosthetic device into a distal end portion of the cinching member to resheathe at least a portion of the prosthetic device and allow repositioning of the prosthetic device relative to the native valve after a portion of the prosthetic device has contacted tissue of a native valve.