In this paper, state estimation for non-linear continuous-time systems is considered in a bounded-error context. The studied systems are described by ordinary differential equations for which explicit solutions are not available. The state estimator built in this paper relies on a validated integration of the ordinary differential equations using Taylor models and on set inversion. This estimator generates the set of all state vectors that are consistent with the modelling hypotheses, the measured data and the noise prior bounds. This property makes the use of this estimator suitable in the field of robust control. To render this algorithm efficient when the initial state is approximately known, consistency techniques are used. An illustrative example is presented.