Assuming you can't switch between normally open and normally closed in your application (for instance, you may want normally open so if the microprocessor loses power the contacts open and you won't have the controlled equipment running continuously!)
Now you can more than halve the power consumption of the energized relay by controlling it with a PWM signal! You energize the relay with digitalWrite(pin,HIGH) for a fraction of a second and then do an analogWrite(pin,127) to power with a 50% duty cycle. Since the load is inductive, this reduces the power by more than 50%.