I connected a DMM in parallel with the battery that is plugged directly into the microphone.
Test 1 = battery charged until the charger LED changed to green, then the battery was removed and left on the shelf for 2 days before testing in the microphoneTest 2 = battery charged for two days (fast charge, then automatic trickle), removed from charger and immediately tested in microphone.
I am slightly disappointed since the battery is supposed to be 250mAh, and I am only discharging it at 50mA ( .2C), so I should get nearly full capacity, but instead only get 200mAh effective capacity when the battery is fresh out of the charger -- 150mAh capacity after a couple days . It will probably be good enough for my application, but this is more evidence that battery manufacturers are inflating their ratings.

I popped open the charger and found a circuit board with a single IC (part number is obfuscated -- possibly not intentionally), lots of SMD transistors and assorted passives.
Here's an oscilloscope screenshot that shows the charging current and voltage behavior. This battery is almost completely discharged. The charger maintains a constant current of 105mA, with a 167ms gap every 1.7 s where no current is put into the battery. Presumably, this is so the charger can monitor the unloaded battery voltage. As you can see, the battery voltage drops from 9.6V to 9.5V in the 167ms gap. As the battery charges, the charge voltage (10 V in this screenshot) rises to accommodate the battery's increasing state of charge.