This paper describes the design of a broadband E-patch antenna using Taguchi method. Although this optimization method exhibits a fast convergence speed, its application to the antenna design has so far been very limited as compared to the particle swarm optimization and differential evolution. Different than the prior work on optimization-based design of E-patch antennas, the presented design is carried out by satisfying multiple objectives: the minimum antenna footprint area and vertical bar S-11 vertical bar < -10 dB bandwidth across 5-6 GHz band. The performance of this E-patch antenna design is compared with that of an E-patch antenna designed with the differential evolution algorithm to meet the same |vertical bar S-11 vertical bar < -10 dB bandwidth criteria. It is shown that a two-level Taguchi method applied to E-patch design problem with 6 degrees of freedom can complete the design with 8 full-wave simulations as compared to the entire 2(6) = 64 possibilities. This is also considerably faster than the differential evolution algorithm that may require > 300 full-wave simulations. In addition, it is shown that the presented design can meet the bandwidth criteria with a smaller footprint, hence demonstrates that minimization of the footprint must also be a part of the design process to achieve the best antenna solution. Furthermore, the E-patch antenna is fabricated and measured to confirm the validity of the proposed design.