Use case: On power loss, the pi is to gracefully close all I/O (already kept to a minimum) and shut down, to be manually rebooted later.
A supercapacitor works (I think; not sure of voltage near the end) but reboots the Pi (not sure why exactly).
A LiPo battery + charger + boost converter work fine, but are overkill. Too many components that could fail, and I need seconds, not hours of runtime.
 The solution linked to by bobstro, and this one, allow the supplied voltage to drop to or below 4V. There are claims that even 3.3V can be OK (here, too), but the specs, I recall, state min. 4.75V. Is lower really safe for the storage? Could change a lot if it was.