Powering Pi Zero + Arduino Micro for brief interruption in supply
As Chris has said. "Engineering" this will be rather difficult. You need to know how much power will be required, and for how long, and furthermore what minimum voltage is acceptable before a reset occurs.

To get good performance, some kind of boost circuit will probably be necessary and basically the whole thing is going to get complicated fast.

So... I'll suggest a practical approach. I'm assuming the gap in power is &lt;1s. Buy as large of a super capacitor as you can reasonably accommodate, and just.. see what happens.

Try a couple of these 5F 5.5v Supercaps: DGH505Q5R5

You may need a few additional parts parts like a diode on the power coming in, or maybe a resistor to limit the inrush current. But I would just start simple and go from there. Let us know if it works.