Abstract Systematic characterization of the shape memory properties of a quaternary Ni 45.3 –Ti 29.7 –Hf 20 –Pd 5 (at.%) polycrystalline alloy was performed in compression after selected aging treatments. Precipitation characteristics were revealed by transmission electron microscopy. The effects of aging temperature and time on transformation temperatures, recoverable and residual strains, and temperature and stress hystereses were determined by differential scanning calorimetry, constant-load thermal cycling experiments and isothermal strain cycling (superelasticity) tests. The crystal structure and lattice parameters of the transforming phases were determined from X-ray diffraction analysis. It was revealed that precipitation hardening significantly improved the shape memory properties of the NiTiHfPd alloy. Under optimum aging conditions, shape memory strains of up to 4% under 1 GPa were possible, and superelasticity experiments resulted in full strain recovery without any plastic deformation, even at stress levels as high as 2 GPa. The NiTiHfPd polycrystalline alloy exhibited very high damping capacity/absorbed energy (30–34 J cm −3 ) and work output (30–35 J cm −3 ), which were attributed to the ability to operate at high stress levels without significant plastic deformation and to a high mechanical hysteresis (>900 MPa) at temperatures ranging from 20 °C to 80 °C.