Resonant heave excitation of tension leg platform (TLP) tendons is typically of high frequency and small amplitude. The response of the tendons to this excitation is non-negligible due to a very small drag coefficient of the structure in this mode of oscillation. Small values of the drag force complicate experimental estimation in a laboratory due to the dominating inertial force. Model tests conducted at the University of Michigan investigating the damping experienced by a cylinder of 0.457 m (1.5 ft) diameter and 1.219 m (4.0 ft) draft are described here. The cylinder is vertical and surface-piercing, and oscillates parallel to its axis. The amplitude of the forcing is varied to give a Keulegan-Carpenter (KC) number range of 0.1–1.0. The frequency parameter β is 89236, corresponding to an oscillation frequency of 0.41 Hz. From these experiments, a definite nonlinear trend is observed between the drag force and velocity conflicting with some of the results reported by Huse (1990) and Chakrabarti and Hanna (1991). The heave damping coefficients of individual structural components of a TLP follow different scaling laws. Rules are presented for scaling friction and form drag components from model to full scale. Results from experiments are used to obtain a scaling law for vertical columns of a TLP. Previously published results are used for horizontal pontoons. An example TLP calculation shows that the heave damping ratio of horizontal cylinders is approximately 0.049–0.078 percent, depending upon cylinder shape, and that for vertical cylinders is in the range 0.025–0.171 percent, depending upon KC.