Backup battery tester circuit
This circuit I showed in the other answer was for when the battery voltage was somewhat higher than the processor's voltage.  After all, that was your original reason for not just connecting the battery to a processor input pin.

When you know the battery voltage won't exceed the processor voltage you can do something like this:



CTRL is driven by a digital output of the processor.  When high, the battery test circuit is off.  when low a few 10s of mA drain is put on the battery, and the battery voltage minus the Q1 saturation voltage appears at out.  This only needs to be on for a few 10s of &micro;s occasionally, so represents very little average drain on the battery.

If the C-E voltage of Q1 introduces a unacceptable offset on the battery voltage reading, then you can replace Q1 with a P channel FET.  You have to make sure to use one that can turn on well enough with just the processor voltage on the gate.  Such things are sometimes called logic level FETs.