Recently, non-circular microresonators have been studied mainly due to their ability to provide long interaction length and ease the air-gap spacing tolerance. The use of rectangular, square-shaped, and/ or polygonal optical microresonators with sharp corners can be limited by severe energy loss at the corners. By incorporating optimum fillet (rounding of corners) design at sharp corners of such optical microresonators optical loss can be eliminated at sharp corners. This results in significantly increasing the quality factor of the round-cornered square-shaped microresonators in comparison to the conventional circular-ring resonator systems. The enhanced quality factor makes the microresonator a promising system that can be used in advanced measurement and detection applications. The two dimensional finite element analysis of the electromagnetic frequency presented in this study quantifies the effect of rotation of round-cornered square-shaped resonators about the coupling region on the quality factor of single-mode resonances in a add-drop configuration system. It is found that the quality factor of these resonators steadily increases with the rotation (0-45° angle) of resonator about the coupling point.