Zener can be good choice.....but I think you can feed 3.7V direclty to your uC, it should tolerate it!! Check the specs in the datasheet, I'm pretty sure it should work out.
the zinner diode will help in case of the the voltage increases but will help in the other case
or
the zinner will provide V of 3.6 what ever the current is
Added after 1 minutes:
Jack// ani said:
Zener can be good choice.....but I think you can feed 3.7V direclty to your uC, it should tolerate it!! Check the specs in the datasheet, I'm pretty sure it should work out.
A shottky barrier diode is just one type of diode. Its advantage in this case is its low forward voltage drop. In order to use as IanP suggested, you have to put it in series with your battery. I think this option is better than using a zener diode.
Make sure that the voltage of the battery you intend to use doesn't go down with it state of charge. Lithium-ion batteries are a good choice, their voltage stays constant until their end-of-life.
You can also use a low-dropout regulator...
I also suggest that you don't try to use 3.7V directly, usually 3.6V is the absolute maximum rating!