Résumé : In PDE-constrained optimization, iterative algorithms are commonly efficiently accelerated by techniques relying on approximate evaluations of the functional to be minimized by an economical, but lower-fidelity model (“metamodel”). Various types of metamodels exist (interpolation polynomials, neural networks, Kriging models, etc). Such metamodels are con- structed by precalculation of a database of functional values by the costly high-fidelity model. In adjoint-based numerical methods, derivatives of the functional are also available at the same cost, although usually with poorer accuracy. Thus, a question arises : should the derivative information, known to be less accurate, be used to construct the metamodel or ignored ? As a first step to answer this question, we consider the case of the Hermitian interpolation of a function of a single variable, when the function values are known exactly, and the derivatives only approximately, assuming a uniform upper bound on this approximation is known. The classical notion of best approximation is revisited in this context, and a criterion is introduced to define the best set of interpolation points. This set is identified by either analytical or numerical means. If n + 1 is the number of interpolation points, it is advantageous to account for the derivative information when Epsilon ≤ Epsilon_0 , where Epsilon_0 decreases with n, and this is in favor of piecewise, low-degree Hermitian interpolants. In all our numerical tests, we have found that the distribution of Chebyshev points is always close to optimal, and provides bounded approximants with close-to-least sensitivity to the uncertainties.