A microstrip patch antenna can be created for terahertz applications where the size of the antenna is shrinking heavily. A device must operate in the THz range, be reduced in size, be of less weight, and be of portable quality, which are strongly supported by the microstrip patch antenna. By virtue of these advantages, microstrip patch antennas can be also designed in different band applications. In this chapter, a rectangular and a square-shaped microstrip patch antenna are designed and compared in terms of some performance metrics like return loss, VSWR, and gain. Both the antennas are designed using two distinct substrate materials: Rogers RT 5880 (εr =2.2) and FR-4 (εr =4.3) with a substrate thickness of 0.70 mm. The inset feed technique is used to design the two of them. The CST studio suite is used to effectively complete all of the replications and analyses for the purpose of terahertz applications at the resonant frequency of 0.105 THz. According to the simulation findings, the Rogers RT 5880 conventional rectangular microstrip patch antenna performs better with regard to return loss and VSWR. However, compared to rectangular antennas, typical square microstrip patch antennas employing Rogers RT 5880 offer superior return loss and high gain. These benefits are crucial for terahertz applications. The square microstrip patch antenna using Rogers RT 5880 having a gain of 7.54 dBi and a percentage bandwidth of 6.22% is then compared with earlier findings that show it has good potential for usage in the terahertz technology.