We demonstrate the measurement of the coefficient of restitution, $e$, for nanoparticles, through observations of the final distribution of bismuth particles that have bounced within silicon V-grooves. The experiments, taken together with complementary molecular-dynamics simulations, show that $e$ is generally smaller for liquid than for solid nanoparticles, and that macroscopic theories underestimate the velocity dependence of $e$. Hence, while nanoparticles are harder than bulk materials, once they have begun to yield the rate of increase of the inelastic deformation is greater.