Here is a schematic diagram of electret microphone pre-amplifier using LMV721 op-amp. because the LMV721 has low noise and low power features, it would be an ideal choice for  battery powered microphone preamplifier. The LMV721 is connected as an inverting amplifier.

battery powered electret microphone circuit schematic

Resistors, R1 =R2 = 4.7k, sets the reference at mid point between VCC = 3V and ground. Thus, this set the op amp for single supply use. The gain of this preamplifier, which is 34dB (50x), is set by resistors R3 = 10k and R4 = 500k. A 10 MHz gain bandwidth product for the LMV721 is more than enough for most audio application since the normal audio range is from 20 Hz to 20kHz. A resistor R5 =5k provides the bias voltage for the electret microphone. Capacitors C1 =C2 = 4.7µF at the input and output is provided to  block out the DC voltage offset. [Circuit schematic diagram source: National Semiconductor Application Notes]