The mechanical impedance of the leg governs many important aspects of locomotion, including energy storage, transfer, and dissipation between joints. These mechanical properties, including stiffness and damping, have been recently quantified at the ankle joint during walking. However, little is known about the human ability to sense changes in impedance. Here, we investigate the ability to detect small changes in damping coefficients when interacting with a mechanical system coupled to the ankle or knee joint. Using a psychophysical experiment (adaptive, weighted staircase method) and an admittance-controlled dynamometer, we determined the 75% minimum detectable change by tasking subjects to compare the damping values of different virtual spring-mass-damper systems. The Weber fraction for damping coefficient ranged from 12% to 31%, with similar performance across the ankle and knee. Damping perception performance was similar to previous stiffness perception results, suggesting that both the stiffness and damping of the environment are important for the human sensorimotor system and motivating further investigation on the role of damping in biomechanics, motor control, and wearable robotic technologies.