We present a variational framework to estimate super-resolved texture maps on a 3D geometry model of a surface from multiple images. Given the calibrated images and the reconstructed geometry, the proposed functional is convex in the super-resolution texture. Using a conformal atlas of the surface, we transform the model from the curved geometry to the flat charts and solve it using state-of-the-art and provably convergent primal-dual algorithms. In order to improve image alignment and quality of the texture, we extend the functional to also optimize for a normal displacement map on the surface as well as the camera calibration parameters. Since the sub-problems for displacement and camera parameters are non-convex, we revert to relaxation schemes in order to robustly estimate a minimizer via sequential convex programming. Experimental results confirm that the proposed super-resolution framework allows to recover textured models with significantly higher level-of-detail than the individual input images.