[cyberferret]

Simplepush looks like a cool service - thanks for the heads up. It seems that it accomplishes the author's main need - that for a constant buzzing which needs to be picked up and dealt with.

EDIT: Just seen that it is Android only! :-/

[ubercow]

If you need something similar that works on iOS (and Android), take a look at https://pushover.net/

I use it for some personal automation scripts that might need to get my attention if something goes wrong.