Serial section electron microscopy (ssEM) is a widely used technique for obtaining volumetric information of biological tissues at nanometer scale. However, accurate 3D reconstructions of identified cellular structures and volumetric quantifications require precise estimates of section thickness and anisotropy (or stretching) along the XY imaging plane. In fact, many image processing algorithms simply assume isotropy within the imaging plane. To ameliorate this problem, we present a method for estimating thickness and stretching of electron microscopy sections using non-parametric Bayesian regression of image statistics. We verify our thickness and stretching estimates using direct measurements obtained by atomic force microscopy (AFM) and show that our method has a lower estimation error compared to a recent indirect thickness estimation method as well as a relative Z coordinate estimation method. Furthermore, we have made the first dataset of ssSEM images with directly measured section thickness values publicly available for the evaluation of indirect thickness estimation methods.