Interesting blog on an experiment to power an Arduino by solar power linked to a capacitor storage system. Nick gets a mention as well 8) Arduino powered by a capacitor - the start - heliosoph
That's nice. 
Plus I have a video of a couple of ultracapacitors powering the Arduino including a lot of LEDs:
I ran an automotive 12v bulb the other day from 2 400F caps (via a step up inverter) it lasted around 40 seconds or so...
And i kinda welded (by accident) a resistor leg to the casing lol
I think the step-up inverter is a good idea, and I think Martin Lorton has a video about just that on YouTube recently.
The problem with capacitors, compared to batteries, is their fairly flat discharge rate. Batteries on the other hand tend to deliver almost the same voltage for a long time, and then it dives down.
Example:
With a step-up inverter you could harness those low voltages (fairly) near the end of the discharge cycle.