I believe that using liquid (coaxial) cell you may be able to measure the melt phase dielectric properties. I also remember to have seen dielectric tests combined with rheology (developed for liquid crystals)
http://www.anton-paar.com/ca-en/products/details/dielectric-spectroscopy/
http://innocentrix.com/files/presentationrheologydielectricmeasurements.pdf
http://cdn.intechopen.com/pdfs-wm/30966.pdf
http://faculty.ksu.edu.sa/othman/Documents/PPS_22_characterization.pdf
the question is how do you make your polymer melt flow, and what is the range of conductivity the polymer has in solid state (what is the polymer system, did you make it conductive using any fillers?). Anyway, you would need to introduce 2 electrodes into the machine where the flow is happening, let me say: just before the die. Then you measure the resistance between the 2 electrodes (need to know their distance in the melt).
There are rheometers out there with the capability of measuring the electrical conductivity and even applying a voltage. The sample could be heated to a specific temperature to gain the desirable fluidity and then the electrical conductivity is measured (such as the ones from Thermo Electron)
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