We characterize planar microcavities in whispering-gallery mode optical resonances. The microcavity consists of a waveguide and a microdisk, and a nanoscale gap separates the waveguide and the microdisk. The devices can be fabricated on \mathrm{Si} -based thin films by using conventional microelectronics techniques. To characterize these types of cavity, we study a broad range of resonator configuration parameters including the size of the microdisk, the width of the gap, and the waveguide dimensions. The finite-element method is used for solving Maxwell's equations. The electric fields and the energy density distributions are obtained and compared between the on-resonance and off-resonance situations. A brilliant ring with a strong electric field and a high-energy density is found inside the periphery of the microdisk under first-order resonance. While under second-order resonance, there are two bright rings, and the light intensity in the inner ring is stronger than that in the outer ring. The resonant frequencies and their free spectral ranges are predominantly determined by the size of the microdisk. The gap effect on the resonant frequencies is observable, although it is minor. The gap strongly affects the full width at half-maximum (FWHM), finesse, and quality factor of the resonances. With an increase in the gap width from 100 to 300\mathrm{nm} , both the Q value and finesse increase substantially, while the FWHM decreases. The waveguide width has a visible influence on the Q value, FWHM, and finesse as well.