We address the inverse problem in Optical Tomography of stably determining the optical properties of an anisotropic medium ¿ ¿ Rn, with n ¿ 3, under the so-called diffusion approximation. Assuming that the scattering coefficient µs is known, we prove Hölder stability of the derivatives of any order of the absorption coefficient µa at the boundary ¿¿ in terms of the measurements, in the time-harmonic case, where the anisotropic medium ¿ is interrogated with an input field that is modulated with a fixed harmonic frequency ¿ =k, where c is the speed of light and k is the wave number. c The stability estimates are established under suitable conditions that include a range of variability for k and they rely on the construction of singular solutions of the underlying forward elliptic system, which extend results obtained in J. Differential Equations 84 (2): 252-272 for the single elliptic equation and those obtained in Applicable Analysis DOI:10.1080/00036811.2020.1758314, where a Lipschitz type stability estimate of µa on ¿¿ was established in terms of the measurements.