I just had one of these moments ...
I was there thinking "why do you need a SIM? Just run it on Wifi and find an app that sends an email/alert to an app on another phone".
Then I just twigged that power out = wifi out = no alert. D'oh indeed!
I'll be setting this up for sure on my next tank.
Alternative app: "Power Failure Monitor Free" (and there are others on there, but this one gets a good review).
[edit] there are apps that can be set to just sound an alarm, which could be still be useful. Just need to be at home to know about it!