We address the problem of determining functional framing from experimental data points in view of robust time-varying predictions, which is of crucial importance in bioprocess monitoring. We propose a method that provides guaranteed functional bounds, instead of sets of parameters values for growth functions such as the classical Monod or Haldane functions commonly used in bioprocess modeling. We illustrate the applicability of the method with bioreactor simulations in batch and continuous mode, as well as on real data. We also present two extensions of the method adding flexibility in its application, and discuss its efficiency in providing guaranteed state estimations.