Thanks for providing the extra info 3v0. I think the needs of battery backup are different from what is normally known as "charging", especially something like cell phone charging.
Normally in battery backup you expect the battery to be trickle charged all the time,a nd be full all the time, with only the occasional power outage where the battery will then supply the power.
If that is the case for your app, I would use one of those tiny low Q-current low drop out 3.3v regulators and always run the device from the battery through the regulator. The regulated voltage will give you some safety and also ensure reliable transmit power and stable performance. Then as for keeping the battery trickle charged that depends on your input power source, mainly what voltage it is.
If your source is 5.0v then I would probably use one or two diodes, normal or schottky as needed to give you approx the right float voltage, then a resistor. Keeping a battery trickle charged from a regulated power source is very easy.
If these are going to be powered all the time I would never consider pumping C/10 into the battery constantly.