In addition to the above, you can use a switcher, then your battery voltage is OK, you just need ramp up your power supply so it gives a tad higher voltage than the battery. OR use a string of high FWD drop diodes from your battery to make the voltage at the junction lower from the battery than from the power supply.

Another option (that I do not like except if you use a processor that is specifoed for 5V and 3.3V) would be to drop the DC/DC or LDO and run the processor at 5V minus the diode drop. Use a low forward drop diode between the power supply and the processor. Then you could use a string of high FWD drop diodes from your battery to make the voltage at the junction lower from the battery than from the power supply. Of course, in this configuration you will have to limit the clock speed to what the processor can handle at 3.3V.

I know that your supply will be more than 3.3V, but I know of no processor that is specified at a voltage in between.

Erik