High-value infrastructure elements, such as bridges, are typically over-designed. Model-updating techniques are useful for estimating the reserve load capacity (beyond safety factors) of bridges and this improves sustainability through good asset-management decision making. In these approaches, measurement data are used to infer model parameter values that influence behaviour. Several approaches have been proposed for structural model updating. Population approaches, such as Bayesian updating, reflect the intrinsically ambiguous nature of diagnosis as well as a range of uncertainty sources. However, many do not consider bias in model formulations, which results in biased identification of parameter values and subsequent predictions. Also, discrete sampling methods may be too coarse to be able to identify critical parts of the population where worst case reserve capacity is determined. In this paper, a new methodology is proposed to update models of structural systems using measurements. This methodology has been employed to identify the most critical set of parameter values for the bending ultimate limit state (ULS) verification and the serviceability limit state (SLS) verification of an existing reinforced concrete bridge after gaining information from measurements. This methodology is based on the error-domain model falsification approach, in which measurements are used to falsify models rather than calibrate them. Through a full-scale case study, it is shown that the new methodology is able to provide a parameter-value set that is more accurate for ULS and SLS verification than those identified with residual minimization. Furthermore, it is shown that residual minimization (traditional curve fitting) may result in unsafe estimates of reserve capacity.