In tele-operation systems, damping is often injected to guarantee system stability during contact with hard objects. In this study, we used psychophysical experiments to assess the effect of adding damping on the user's perception of object hardness. In Experiments 1 and 2, combinations of stiffness and damping were tested to assess their effect on perceived hardness. In both experiments, two tasks were used: an in-contact task, starting at the object's surface, and a contact-transition task, including a free-air movement. In Experiment 3, the difference between inserting damping globally (equally throughout the workspace) and locally (inside the object only) was tested. In all experiments, the correlation between the participant's perceptual decision and force and position data was also investigated. Experiments 1 and 2 show that when injecting damping globally, perceived hardness slightly increased for an in-contact task, while it decreased considerably for a contact-transition task. Experiment 3 shows that this effect was mainly due to inserting damping globally, since there was a large perceptual difference between inserting damping globally and locally. The force and position parameters suggest that participants used the same force profile during the two movements of one trial and assessed the system's reaction to this force to perceive hardness.