For experimental measurements, you may try capacitance and dielectric constant measurements using a LCR meter.  

The common experimental techniques are UV-VIS-IR  spectrophotometer or Spectroscopic ellipsometry 

Hello,

your question is not complete.

you should precise the frequency at which you want this constant.

At high frequency, optical methods are ok (UV-VIS-IR). At low frequency you should use dielectric measurements (through impedancemeter or LCR meter). Both values are different, one includes only the response of electrons, the other one the response of electrons and ions (highly polarisable in some cases).

Theoretical methods (DFT, classical potentials like implemented within GULP) are in principle able to calculate both.

hoping it helps

Guilhem

You can use dielectric measurements (L,C,R-meter, impedancemeter etc.).