In the field of electromagnetism, there are materials known as metamaterials which exhibit unique properties that can be exploited. Permittivity, defined as capacitance per meter, of a metamaterial can vary over frequency , time, or even be negative. This can be useful for tuning antennas, changing their operating frequency or direction of propagation, or even designing cloaking systems. However, the theory behind metamaterials needs to be studied further. One of the biggest issues to address is in determining the constitutive parameters of metamaterials which may be varying. Previous research has shown the issue of branches, or mathematical discontinuities, occurring in the derivation of permittivity from the scattering parameters of a metamaterial. This thesis provides further understanding to the theory behind these branches and presents a new method to compensate for them. This new method, called the phase tracking method, may be considered a modern adaptation of the Nicolson-Ross-Weir method.