Two dielectric waveguides that are evanescently coupled to a square or rectangular region of increased refractive index can serve as a very compact integrated optical microresonator. We consider these devices in a spatial two-dimensional setting, where a rigorous mode expansion technique enables accurate and quite efficient numerical simulations of these configurations. The paper is concerned with single resonator units as well as with an add-drop filter constructed by cascading two square cavities. Besides calculating the power transmission spectra, we try to document as far as possible the characteristic electric field patterns that occur at major and minor resonance wavelengths. The influence of the various geometrical parameters on the resonator performance is investigated in detail.