Surge damping systems (135) and processes for using same. In some embodiments, a system (100) for mooring a vessel (105) includes a mooring support structure (150) that includes a base structure and a turntable disposed on the base structure. A vessel support structure is disposed on the vessel. At least one extension arm is suspended from the vessel support structure. A ballast tank (130) is connected to the extension arm. A uni-directional passive surge damping system is disposed on the vessel and includes an elongated tension member (132) connected to the ballast tank that is configured to dampen a movement of the ballast tank by applying a tension thereto. A yoke (110) extends from and is connected at a first end to the ballast tank and includes a yoke head (115) disposed on a second end thereof that is configured to connect to the turntable.