This paper is about parameter estimation for models described by a continuoustime state equation from discrete-time measurements. Guaranteed solutions to this problem are proposed in probabilistic and bounded-error contexts, based on Müller’s theorems and interval analysis. In a probabilistic context where parameter estimation boils down to parameter optimization, this makes it possible to characterize the set of all globally optimal parameter vectors. In a bounded-error context, this allows the characterization of the set of all parameter vectors that are consistent with the error bounds, measurements and model structure. The resulting methodology is illustrated on a simulated example of anaerobic fermentation process.