We address the stability issue in CalderOn's problem for a special class of anisotropic conductivities of the form sigma = gamma A in a Lipschitz domain Omega subset of R-n, n >= 3, where A is a known Lipschitz continuous matrix-valued function and gamma is the unknown piecewise affine scalar function on a given partition of Omega. We define an ad hoc misfit functional encoding our data and establish stability estimates for this class of anisotropic conductivity in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map.