A solenoid assembly includes a solenoid having a coil provided with a passageway and a plunger movable within the passageway upon application of electrical power to the coil. A frame holds the solenoid and includes a backstop movably mounted in the frame extending into the coil passageway. The backstop is selectively engaged by the plunger such that the backstop and the plunger are subjected to an impact therebetween. A resilient dampening element is positioned between the frame and the backstop for cushioning the impact between the backstop and the plunger.