Superconducting Josephson junctions have major advantages as detectors of millimeter wave radiation. Frequency of the radiation can be easily derived from the Shapiro steps of the current-voltage characteristics. However, system performance is highly sensitive to impedance mismatch between the antenna and the junction; therefore, optimization is essential. We analyzed and implemented an improved antenna structure, in which the junction is displaced from the antenna center and placed between the ends of two matching strips. Based on theoretical analysis and advanced electromagnetic simulations, we optimized strip dimensions, which affect both the detection magnitude and the frequency of the reflection coefficient dip. Accordingly, two Au bow-tie antennas with different matching strip widths were fabricated. Superconducting Yttrium Barium Copper Oxide (YBCO) thin films were deposited exactly at the bicrystal substrate misorientation points, forming Josephson junctions at the ends of two matching strips. We found a very high correlation between the simulations and the response to Radio Frequency (RF) radiation in the range of 145–165 GHz. Experimental results agree extremely well with the design, showing best performance of both antennas around the frequency for which impedance matching was derived.