The re‐centring capability is recognized as a fundamental function of the isolation system, because it is intended to prevent substantial permanent deformation at the end of the earthquake that may affect the serviceability of the structure and eventually limit the capability of the isolators to withstand aftershocks and future earthquakes. In this study, the re‐centring behaviour of isolation systems composed of sliding bearings with curved surfaces is investigated in shake‐table tests carried out on a one‐storey steel frame with rectangular plan, scaled at one third‐length scale and isolated with four bearings. The coefficient of friction of the bearings is varied by changing the material or lubrication condition of the pads, providing different equivalent damping ratios to the isolation system. The response of the base isolated structure to selected natural ground motion waveforms is assessed in terms of the residual displacement after a single event and the accrual of displacements during a sequence of quakes, and considerations on the influence of the coefficient of friction on the re‐centring behaviour, as well as on the effect of an initial displacement offset are drawn. The re‐centring provision of the current European design code is eventually checked against the experimental data. Copyright © 2016 John Wiley & Sons, Ltd.