Global sensitivity analysis is often impracticable for complex and time demanding numerical models, as it requires a large number of runs. The reduced-basis approach provides a way to replace the original model by a much faster to run code. In this paper, we are interested in the information loss induced by the approximation on the estimation of sensitivity indices. We present a method to provide a robust error assessment, hence enabling significant time savings without sacrifice on precision and rigourousness. We illustrate our method with an experiment where computation time is divided by a factor of nearly 6. We also give directions on tuning some of the parameters used in our estimation algorithms.