Apparatus embodying the invention include a damping plate attached to the submerged end of a spar-like element floating in a body of water. The spar like element tends to move up and down in a vertical direction in response to passing waves. The damping plate has a pair of oppositely facing surfaces extending transversely to the vertical direction of the movement of the spar-like element and vertical structures (“lips”) mounted on the oppositely facing surfaces for increasing the effective mass of water pushed during movement of the damping plate through the water. Damping plates with lips, as per the invention, may be used in wave energy converters to control the relative motion between the spar-like element and a float to increase the energy produced.