New (I think) supercap..could be useful.

[SXRguyinMA]

...Biggest I ever used were a handful of 10F/5V supercaps (each a bit bigger than my thumb) from SparkFun...

like these?

[Konrad]

Hmmm, mine were bigger, SXR, I'd say about 3" length and .75" diameter, maybe a shade larger. And covered in big fat white lettering "10F/5V" - couldn't miss it. Cost about $5 each in 2006, I think, though I just looked at SparkFun and can't find 'em. Yours are newer tech though, maybe the same punch in a smaller package.

[SXRguyinMA]

well these are the ones I used, and they're 10F/2.5V instead of 5v as well