We present a noninvasive optical method to measure the oxygen saturation of hemoglobin in breast lesions. This method introduces the novel concept that the best choice of near-infrared wavelengths for noninvasive tumor oximetry consists of a wavelength pair (lambda1, lambda2) within the range 680-880 nm, where the specific values of lambda1 and lambda2 depend on the optical properties of the specific tumor under examination. Our method involves two steps: (1) identify the optimal wavelength pair for each tumor and (2) measure the tumor oxygenation using the optical data at the two selected wavelengths. We have tested our method by acquiring experimental optical data from turbid media containing cylindrical or irregularly shaped inhomogeneities and by computing theoretical data for the case of spherical lesions embedded in a highly scattering medium. We have found that our optical method can provide accurate and quantitative measurements of the oxygenation of embedded lesions without requiring knowledge of their size, shape, and depth.