Can you use a supercap to keep a microcontroller alive while changing batteries

[alank2]

Let's say I am using a CR2032 to power a microcontroller at 3V.  If it is in a very low power mode, can a supercap be used to keep it alive for X seconds while doing a battery change?

How would it be connected in circuit?  Just like a regular capacitor?  Before or after a PTC?  If you know the power consumption, is there a formula for calculating how long it will last?

[brucehoult]

Sure, why not?

If you take 1 Amp of current out of a 1 Farad capacitor then the voltage changes by 1 Volt/s.

So for example if you have an MSP430 drawing 6 µA in standby mode, and a 100 µF capacitor (which costs about 50c) then the voltage will drop by 0.06V/s.