keep voltage like "ups" for 8051

I have a project where i must keep μΕ active for a "little" time till i write to EEPROM some serious staff from RAM and dont get lost. I found a solution with capacitor and INT0 interrupt..Any other idea or any help on code ?

capacitor is fine but you need to use a big cap for a good amount of time. e.g. usually eeprom require max 5ms time for a write operation to complete. If you are not doing a block write (bunch of bytes at a time) then it may take longer for you.

Second option could be to use a small backup battery only for controller and EEPROM, but again you have to add another circuit to maintain that battery (charging etc).

I think you can consider using a capacitor if your timing is small enough and capacitor is big enough to supply power for that much time. You can do some trials with different capacitors and see how long they last at a particular voltage.