In this paper, Antipodal Vivaldi antennas with enhanced directivity using Anisotropic Zero Index Metamaterial (AZIM) are presented. These antennas are needed in order to implement a compact small Synthetic Aperture Radar (SAR) that operates at 3.35 GHz. The main goal is to enhance the antenna's directivity using AZIM with the Antipodal Vivaldi antenna with a size shorter than 3Ȝ0 (Ȝ0 is the corresponding wavelength of the operational frequency), which is a typical size in many publications. Challenges and disadvantages to carry out this research are presented. A discussion on making a comparison among three antenna prototypes where AZIM was embedded is also presented.