This computational parametric study analyzes the effect of geometrical design parameters of a microring resonator on its optical characteristics with the goal to optimize its performance for label-free detection of biomarkers. Electromagnetic frequency domain analysis was performed using finite element numerical technique for the microring resonator. Effect of the width of feed and pickup waveguides, the coupling gap between the waveguide and microring, and the outer radius of microring on the quality factor were analyzed and quantified for a narrow operational range of wavelength between 1309-1311 nm. The computational simulation showed that these parameters play an important role in avoiding the loss of electromagnetic field, while increasing the effective circulation of energy in the resonator, the ability to achieve multiple single-mode resonances within certain wavelength bandwidth, and the quality of output signal for detection. As a result, the quality factor was enhanced by an order of magnitude with the obtained optimum values of waveguide width, coupling gap, and microring radius without changing the material of resonator or waveguide, and the medium surrounding the resonator. The ability to optically detect a nanoparticle representing a cell vesicle was demonstrated. This enhanced quality factor of the resonator will allow highly sensitive and rapid detection of biomarkers and measurement of their size.