Computing the maximal pose error given an upper bound on perturbations is challenging for parallel robots, mainly because the direct kinematic problem has several solutions, which become unstable near or at parallel singularities. In this paper, we propose a local uniqueness hypothesis that will allow safely computing pose error upper bounds using nonlinear optimization. This hypothesis , together with a corresponding maximal allowed perturbation domain and a certified pose error upper bound valid over the complete workspace, will be proved numerically using a parametric version of Kantorovich theorem and certified nonlinear global optimization. We will then show how to synthesize tolerances reaching a prescribed maximal pose error over a workspace using approximate linearizations. This approximate tolerance synthesis will finally be checked using the certified pose error upper bound we propose. Preliminary experiments on a RPRPR and a 3RPR with fixed orientation parallel manipulators are presented .