There are also this tiny caps 100,000uF/5.5v.

or if you have some little more space, 1Farad/5.5v.
(1,000,000uF/5.5v) these are very small compared to the cap size.


If you can use one of these tiny ones, you can have your PIC running for hours when the battery goes off; but to know for how long it would last with a LED in ON state, you need to try.


----------------------------------