In this paper, a new formulation of the problem of mass and energy balance equilibration in the case of unknown-but-bounded errors is proposed. The bounds of the errors are specified over both a measurement noise and the balance equations. Both bounds are mainly motivated by experimental considerations of the measurement precision; with a more general interpretation, they can be considered as parameters that the user has to adjust to make the reconciliation possible. The method is particularly suitable for linear models but has been extended to nonlinear ones as well. Simulations provide results that compare favorably with those of classical reconciliation methods involving maximum likelihood estimation based on statistical knowledge of the measurement errors.