Resonator-based optical sensors detect the change of refractive index in the environment by measuring the resonance shift. The sensitivity of such sensors is determined by how precise one can locate the resonant wavelength, which is thought to be limited by the bandwidth and the quality factor of the resonator. Here we show that, with a tunable resonator, one can determine the resonant wavelength with ultrahigh precision. Using a silicon microring resonator with an embedded p-i-n junction for electro-optic tuning, whose quality factor is only 14,000, we measured the resonant wavelength with a resolution of 0.06 pm, which corresponds to an index sensitivity of ~10(-7). This resonance measurement for sensing purposes can be done using a fixed-wavelength laser.