You can create a circuit that measures the phase and amplitude across a 100 ohm resistor in series with the crystal. A 56 ohm resistor should shunt the generator input to provide termination for the generator. You must also measure or project the shunt capacitance of the crystal and cancel it out with an inductor across the crystal.
Normally a vector voltmeter would be used to measure the voltage and phase at either end of 100 ohm series resistor to ground. You could use an oscilloscope but levels necessary to read amplitude on a scope may be too high for the crystal. Too high a drive level may damage the crystal.
If you correctly cancel out the shunt capacitance of the crystal you will measure the amplitude and calculated current at zero phase crossing, along with the series resonant frequency of the crystal. You then install a series cap, about a 20 pF for a 10 MHz AT cut crystal, and adjust the freq to achieve zero phase resonance again. You now have all the info to calculate Lm and Cm of the crystal. The change in series resonance with the known value 20 pF predicts what the Lm and Cm values must be to get the measure frequency shift.
The shunt capacitance of crystal can be measured at low frequency. For a 10 MHz AT cut it will likely be in 4 to 6 pF range. If you only have a DVM with capacitance metering, use a known 5 pF cap to help calibrate the DVM reading, as the DVM may not be very accurate on its own at 5 pF range.