I think if you can measure the permittivity, then you must have an LCR bridge. using the latter:
1- measure the impedance of your sample, if it is >100kohm then go to 3
2- if your impedance is <100 kohm then measure the following parameters, using your LCR bridge, Cs, D or Q, or better theta.
3- measure Cp,  D or Q, or better theta.
Now you have some data for certain frequency range, you can start calculation.

4- if your D or Q values are within the limits of the bridge, it is easier, so I'll assume this for now & we'll call option A:
using the cell of your measured sample,measure the same Capacitance for the air, Cs or Cp.
Or you can calculate it using your sample cell dimensions.

Now 
* divide all the measured Cs or Cp by the value for the air. you can get the permittivity
* multiply the value of D or 1/Q by all the permittivity values you have. you you have the Loss (Imaginary part of the permittivity).
* Apply the relation conductivity=2PiF EoE''.
then you're there.
hope this is easy to follow.
Kind regards