Measure the current draw of the microphone. Very often, this type of microphone uses an "electret condenser" microphone capsule. And due to the incredibly high output impedance of a tiny condenser element, they use a FET or low-power, high input impedance Op Amp to buffer the signal so it will work with typical 600 ohm systems. But that's the only thing that draws any current in the system.
As a result, these microphones usually draw very little current. Frequently well below 1 mA. But measure yours to be sure.
Also, check the documentation to see what range of voltages the microphone is designed to use.
Let's assume that the mic draws 1mA of current. If we can live with, perhaps, 2 Volts of voltage loss in our filter, you can increase the value of your filter's resistors to be 1K each. You will still want higher value capacitors, but at least they won't need to be huge!
Using a couple of 1K resistors and a couple of 2200uF caps, you might get rid of the 120Hz ripple fairly well.
Of course, this low current drain also means that a battery will last quite a while, too.
And you may find that the current draw of the mic is even lower than our 1mA figure, so you could use even higher value resistors.
Another option is to build a simple series voltage regulator circuit for the mic. I still like the venerable LM317 adjustable regulators for a lot of audio uses. They're surprisingly fast, so they're suitable for "hi fi" use when you bypass them properly with high-quality capacitors. They'd certainly be just fine for one of these mics. You can get the small TO-92 package LM317LZ versions for very cheap. Add a couple of resistors and a couple of caps, and you've got a very respectable voltage regulator suitable for this use. It might actually end up being cheaper than the higher value capacitors you'd end up needing to use to build a passive filter.
And finally, some small wall-warts actually have decent linear regulators built into them, and can be quiet enough on their own for this sort of use.
Sometimes having high quality audio is quite important for a security camera setup. So it may be worthwhile to provide a good clean supply for the microphone.
This all makes me wonder if there would be a market for a good quality microphone with built in compression amplifier made to plug into these security cameras. Having the audio already compressed before it hits the camera could eliminate that annoying clipping (hard limiting) that you tend to get when a loud vehicle goes by, or the wind hits the mic. We tend to worry a lot about the video quality from our cameras, and then blow off the audio end of things. But it can be important.
