A mooring latch includes a passive foundation portion and a latching portion. The latching portion includes a mechanism, a conical surface shaped to mate with a conical surface of the passive portion, a connector for connection to a mooring structure and permitting rotation about a horizontal axis. The mechanism has a latched configuration that mates the conical surfaces and permits rotations about a shared vertical axis of the conical surfaces. A mooring line threaded through the passive and latching portions and equipped with one or more stops may be used to guide the latching portion to or from the passive portion and to actuate latching or unlatching or the mooring latch.