A vertical damping system for a plurality of water vessels for diminishing the relative vertical movement between two or more water vessels moored in a skin-to-skin orientation. The vertical damping system may include one or more vertical damping devices, each device pivotally connected to a side portion of a first vessel and detachably connecting to a side portion of a second vessel. The vertical damping device may be a piston/cylinder arrangement and the damping system may involve more than two water vessels. The vertical damping system counteracts the effect of roll motion on water vessels, thereby enabling ship-to-ship functions such as cargo loading and the like.