Accurate models of real behaviour that are determined through measurements help engineers avoid expensive interventions and structural replacement. Model calibration by “curve-fitting” measurements to predictions is not appropriate for full-scale structures. This paper compares two population methods that can include modelling and measurement uncertainties using a simple example of a one-span beam. Standard applications of Bayesian inference that involve assumptions of independent zero-mean Gaussian distributions may not lead to accurate predictions, particularly when extrapolating. Another method, error-domain model falsification provides more reliable, albeit more approximate, predictions – especially when prediction is extrapolation. An example of a full-scale bridge illustrates the usefulness of the methodology in a real situation through improvements to fatigue-life estimates compared with design-type calculations without measurements.