In the case of nanocrystals you can measure only the dielectric porperties of powder aggreggates or dilute suspensions/dispersions e.g. in insulating liquids. From the latter you can calculate back the dielectric properties of the inclusions if you know the dielectic properties of the suspending liquid. It has some inaccuracies, however. The mixture formulae are not fully exact, therefore the result you obtain will depend somewhat on the fomula you choose. The other problem is that the mixture formulae are based on continuum theories. In the case of nanonparticles, however, you are at the limit of continuum theories, therefore you will obtin a kind of "effective" dielectric parameter for the filler. I attach an article on dielectric mixture formulas.
Herein, You will find in the appended link my new article which will give you all dielectric parameters and the relation between them, in addition some other parameters.