Raspberry Pi Super Capacitor On Battery Loss
The latest Pi 3B+ has no fewer than six different voltage rails: 


two at 3.3V — one special ‘quiet’ one for audio, and one for everything else; 1.8V; 
1.2V for the LPDDR2 memory; and 
1.2V nominal for the CPU core  with dynamic control
then 5V for USB etc.
some use the XR77004 chip to create all the voltages.
some rPi's use a solid 2.5A supply @ 5V


Verify all your assumptions before you plan a solution by monitoring the worst case current.

Backup and redundancy must be carefully done and tested under all possible situations to be sure it does not create a new problem during the transition or due to high ESR caps.

The voltage dtop from any battery or capacitor in the linear region is **dV=Ic/C * dt + ESR * R ** 

This means the voltage drops 1st from cap ESR then accumulates with time dt (s) at the rate of Ic/C.

So at 1A / 100 Farads will drop 10mV/s or 100mV/10s per Amp load current.

it is normal for DC-DC input current to rise as the input voltage drops to support a constant power load. 

Although CMOS draws less current at some frequency with reduced voltage, but the DCDC converters may need more current to maintain all the outputs when your supply fails.

Good luck.