We measured the dynamic damping of a pair of flapping cicada wings mounted on a robotic insect thorax mechanism capable of high frequency flapping. The damping coefficients were derived based on the measurements of the wing-thorax mechanism translating along its body principal axes. The robotic mechanism has a 10cm wingtip-to-wingtip span, flaps up to 65Hz, and weigh 2.86 gram including the motor and wings. To measure the flapping induced damping during translation, we developed a pendulum system mounted with encoder, and attached the flapper at the end and in different orientations such that its motion is along its principle axes. The damping of the flapper is then calculated from the decaying rate of the magnitude of the oscillating pendulum. The damping coefficients calculated from the experiments are very close to those estimated based on our mathematic models using Blade-Element Theory (BET) and quasi-steady aerodynamic models. As expected, the damping linearly increases with the flapping frequency and is most prominent along forward/backward direction.