The UPS

The DC source I picked is the PYB10-Q24-S12-U DC-DC converter. It has wide input range (9-36V), ideal for a lead-acid battery, or any number of UPS's, and has a sufficient current output (833mA) at 12V to supply both boards. On top of that, it has 1.5kV isolation between input and output, which I wanted to isolate the boards as completely as possible from the UPS and PC interface (since the boards are still techinically tied to the mains via the neutral wire, even if the live wire is not present).

To power the boards, and PC interface, I chose a no-name generic 18650 Lithium cell UPS:

[Pic of UPS from ebay here]

It can be charged from a 5V/2A USB power supply, which I have far too many of already, and outputs a steady 12V at 1.2A (max). Simply install your preferred brand and capacity of 18650 cell and off it goes.