A swing energy recovery system for a machine is disclosed. The swing energy recovery system may have a pump configured to pressurize fluid, a motor driven by a flow of pressurized fluid from the pump, and an energy recovery arrangement configured to receive pressurized fluid discharged from the motor and selectively supply pressurized fluid to the motor. The swing energy recovery system may also have a pressure relief valve associated with the motor, and a controller in communication with the energy recovery arrangement and the pressure relief valve. The controller may be configured to selectively adjust a setting of the pressure relief valve based on an operating condition of the energy recovery arrangement.