This article presents bounds on radiation efficiency and gain for microstrip patch antennas, demonstrating close alignment with the performance of classic antenna designs. These bounds serve as effective benchmarks for assessing antenna performance and evaluating trade-offs and design feasibility. The study particularly addresses the trade-off between miniaturization and performance by comparing bounds for antennas of similar size and frequency, achieved either by using high-permittivity substrates or by optimizing the metallic patch design area. To enhance usability, scaling laws are applied, enabling these bounds to be approximated across a range of frequencies using only data from a half-wavelength patch antenna simulation or measurement. Additionally, the study finds a strong correlation between the established radiation efficiency bounds and lower Q-factor limits (indicative of maximum bandwidth). This relationship is highly advantageous in the design process, as it illustrates how bandwidth and radiation efficiency can be optimized together.