In the event of a power outage, you have two main issues - gas exchange and temperature.
The best approach when money is available is a generator and a transfer switch.
The poor man's approach is a battery-operated air pump and a blanket.
I have an air pump that plugs into a normal outlet. When the outlet goes dead (power outage), the air pump turns on and sends air theough two airstones in the tank.
If you expect a prolonged power outage to result in significant loss of temperature in the room, covering your tank with blankets will keep it from cooling down as quickly.
The best approach mentioned above will keep everything as close to normal as possible. The poor man's approach will at least buy time and allow you to make it through reasonable power outages.