We describe tunable-optical-filter-based white-light interferometry for sensor interrogation. By introducing a tunable optical filter into a white-light interferometry system, one can interrogate an interferometer with either quadrature demodulation or spectral-domain detection at low cost. To demonstrate the feasibility of effectively demodulating various types of interferometric sensor, experiments have been performed using an extrinsic Fabry-Perot tunable filter to interrogate two extrinsic Fabry-Perot interferometric temperature sensors and a diaphragm-based pressure sensor.