Fuel cells play an important role in reducing environmental impacts to produce cleaner electricity. Numerical models are used to simulate their performance and build efficient observers in real use. The accuracy of these models is a major concern, as they can be parameterized by several values. Most of the previous works study the estimation of these parameters using various metaheuristics. While these methods are stochastic and do not provide any proof of optimality, the current paper introduces a global optimization method to accurately bound the optimal root mean square error between the parameterized model and some experimental data. The proposed algorithm is based on a deterministic Interval Branch-and-Bound optimization (IBBO) framework. Interval arithmetic ensures set-based computations to safely bound the objective function value. Four types of fuel cells, with their experimental data, are used to demonstrate the efficiency of the proposed methods. IBBO results are compared with some competing optimization methods used in the literature. They show a better accuracy for the computed feasible solutions (upper bounds) and a guaranteed value of the best possible solutions (lower bounds). This last information is not possible to obtain with metaheuristic algorithms. Compared to other Branch-and-Bound algorithms, IBBO proposes a new mix of mechanisms (e.g. advanced constraint propagation, specific search heuristic and feasible point finding method). Due to the deterministic nature of IBBO, results can be repeated. Its convergence analysis is detailed on four fuel cells from which a real test system based on Scribner technology is used to demonstrate the accuracy and robustness of IBBO on several usage scenarios.