We present a method for determining the core and cladding refractive indices of a microring resonator from its measured quasi-transverse electric and magnetic resonant modes. We use single wavelength reflective microrings to resolve the azimuthal order ambiguity of the measured resonances. We perform accurate electromagnetic simulations to model the dependence of the resonances on geometrical and material parameters. We linearize the model and use the singular value decomposition method to find the best fit parameters for the measured data. At 1550 nm, we determine n(Si(3)N(4))=1.977±0.003 for stoichiometric silicon nitride deposited using low-pressure chemical vapor deposition (LPCVD) technique and n(SiO(x))=1.428±0.011 for plasma-enhanced chemical vapor deposition (PECVD) oxide. By measuring the temperature sensitivities of microring resonant modes with different polarizations, we find the thermo-optic coefficient of the stoichiometric silicon nitride to be dn(Si(3)N(4))/dT=(2.45±0.09)×10(-5) (RIU/°C) and the PECVD oxide to be dn(SiO(x))/dT=(0.95±0.10)×10(-5) (RIU/°C).