in a research experiment to fabricate metamaterial, what is the procedure to determine both mu and epsilon, especially the mu and epsilon near zero (MENZ)?
There are several methods to do it. But the most common is the calculating reflection and transmission coefficients, scaterring matrix. So, if you have reflection and transmission coefficients, you can calculate refractive index and impedance. Using these parameters you can define effective permittivity and permeability. You can find more information and formulas in this article (http://journals.aps.org/prb/abstract/10.1103/PhysRevB.65.195104), for example. Good luck!