For measuring the back emf of the motor, do you have any other good method? I don't have anything to couple one motor to the other. Not sure if the method presented in:
http://electronics.stackexchange.com/questions/54997/how-can-i-measure-back-emf-to-infer-the-speed-of-a-dc-motor
is valid. While the motor was spinning, I measured the voltage (Vrm) across the motor. Since the current was fairly constant, I could ignore L. So, no voltage across the inductor. In my case, I connected the DC source directly to the motor. Thus, the duty cycle is 100%. Voltage effectively applied to the motor is 9V (the source input voltage). Voltage drop over motor resistance is the Vrm. Back EMF is then 9V-Vrm. Is this acceptable?
Back EMF will obviously vary with load but the internal resistance of the motor probably doesn't change a lot. So, Ohm's Law still applies as does Kirchoff's. You know the internal resistance and, absent back EMF, the current would just be the applied voltage divided by the internal resistance. What you will actually read is the applied voltage MINUS the back EMF (voltage) divided by the internal resistance. As you load the motor, you expect the current to increase and, when it does, the only possible interpretation is that the back EMF is reduced at that load.
Obviously, the motor needs to be running to measure back EMF and the source needs to be sufficient to drive the motor at load. So, it is necessary to measure both the motor terminal voltage and current at the same time just in case the battery internal resistance starts to be a factor (and it will). Once you get voltage and current versus some load (how to measure?), you will have a graph for back EMF.
Applying a load is non-trivial. Something like a Prony Brake is usually used. Something like a slipping clutch with a lever arm attached to a scale.
Unloaded back EMF is interesting but since the value changes dramatically from no-load to full-load, it would seem to me that multiple measurements are desireable. Or, you can straight line the graph from unloaded back EMF at some RPM (to be measured) down to 0V back EMF at 0 RPM. I doubt that the straight line graph is true anywhere except the end points.
Your DMM will add inductance (and a small bit of resistance) to the circuit. I would ignore it. Assuming the motor is sufficiently small, just use the meter 10A current scale for a very short period of time (RTFM).
All of the above gets you back EMF. To get inductance, use the other procedure of applying a sine wave and looking at the phase shift between voltage and current. I'm less comfortable with this measurement. Inductance is a function of frequency and this is typically measured with a nice clean sine wave. The motor is almost never driven this way. Square waves (from PWM) have harmonics so which frequency are we talking about?