In a method of and apparatus for offshore mooring, a clamping apparatus includes a clamping mechanism and a pulley. A mooring line connected to an anchor or a pendant line connected to a vessel to be moored extends through the clamping mechanism and around the pulley of the clamping apparatus. The distal end of the line extending through the clamping apparatus is connected to an anchor handling vessel. The anchor handling vessel is employed to apply a predetermined tension to the pendant line and the preset mooring line. A remote operated vehicle is then employed to actuate the clamping apparatus and to disengage the anchor handling vessel.