Model updating attempts to correct errors in a finite element model using measured data. However, the measurements are corrupted with noise and the finite element model contains errors. Most updating schemes try to find the best model in some mean sense. This paper takes a different view and uses robust estimation techniques to determine the most robust parameter set. This parameter set is optimum in that the residuals are as small as can be, for a range of bounded uncertainties on the model and measurements. The relationship between this robust identification and Tikhonov regularisation is explored. The use of the 'L' curve method and expected parameter uncertainty to determine the regularisation parameter are shown. The approach is demonstrated using a simulated cantilever beam example, and experimental data from the GARTEUR test structure.