Dear Sudhakar, Your question is not clear. If u have a dielectric material then you have to find the dielectric properties by using a method which is suitable to your material. It can be coaxial probe methods for liquid or semi-solids (in broadband frequency region) or cavity/wave guide method for single frequency (specially for solid materials). There are other methods also include free-space methods etc. It depends upon your material type, frequency range and whether you are using vector network analyzer , impedance analyzer or klystron tube for a set up bench. While VNA will give automatic values of real and imaginary part, you have to manually calculate the real and imaginary part for microwave set up bench by making use of resonant frequency.

Try to read the enclosed paper to understand the Cole-Cole plot analysis

You have to know the right order of your work. First, you need to collect the real and imaginary parts of the impedance at different frequencies by using the impedance spectrometer. Then, the cole-cole plot can be created.

impedance measurements and capacitance (for dielectric) measurements are different.

For impedance you apply a small signal ac voltage, measure the current (amplitude and phase) and get the impedance, which is a complex quantity.

and varies with frequency.

For dielectric constant, there are many different methods for capacitance measurement. A practical capacitor is represented as a capacitance with a resistance in parallel. For an ideal capacitor the resistance is infinity, but all practical capacitors have a finite resistance, which represent the loss factor of the dielectric capacitor.

However you can estimate the equivalent capacitance of you capacitor from impedance measurement, by fitting the Cole-Cole impedance plots with an appropriate equivalent circuit. Read the enclosed paper to learn this technique to estimate your capacitance from the impedance measurements. The enclosed is available on the net.