A floating mooring system for a single CycWEC applies counter forces and torques to keep a generator suitably stationary for power generation without requiring fixed attachments to the ocean floor or requiring a large frame interconnecting multiple CycWECs. The mooring system uses floats or floatation structure with differential ballasting to counter operating torque and drag plates to counter reactive forces. The floatation structures may be used to float the CycWEC for transport to a deployment location, where changing the overall ballasting of the floatation structures submerges the CycWEC to a desired depth and differential ballasting in the floatation structures counts expected operating torques.