If you use a motor driver that has an enable/PWM input you can use PWM (pulse-width modulation) to run the motor at a lower effective voltage. This is much more efficient than using a voltage regulator.
If your motor is rated for 3V then the maximum PWM duty cycle should be about 3/11.1 = 27%. Using the analogWrite() function to generate PWM means you should call this function with values analogWrite(0) (motors off) to analogWrite(69) (about 27% of 255, the maximum value).
The Rugged Motor Driver
: two H-bridges, more power than an L298, fully protected