Short term? I've got a battery powered air pump and a couple of air stones that I can toss in to keep water moving for gas exchange. If the power drops for an hour or two, that's good enough for me. Long term is another matter entirely.
We get storms that down powerlines around here fairly regularly. I'm rural... very rural... and have had to deal with power outages as long as 11 days. Thankfully, that was once, and a decade ago... I hope to never do that again. Anyway, a decent gas generator was really my only option. Natural gas is not available here, and with the price fluctuation that propane is known for... gas it is. My 6000 watt generator is mounted to a small trailer, can be towed out of the garage by my four wheeler, stationed under the car port in front of the house. A few extension cords, and we're as comfortable as we're going to be. It's not an ideal solution, rather inconvenient, when we need it, but it works for us. I have a pellet stove in the living room. Plug that into 110, and it will keep the front half of the house nice and toasty, the back half livable, if a bit cool. The only thing I run on my tank would be the return pump and heater. System can live without skimmer, lights, ATO, etc. for quite some time. As long as the flow keeps flowing, and the temperature stays reasonable, it'll be fine.
If I lived in town, where natural gas was available? I'd have a natural gas whole house generator with an automatic transfer circuit installed in a heartbeat. Yes, it's going to cost you some money, but knowing that you can get on with life as usual during a power outage is one heck of a warm fuzzy feeling.