Cut-off lows that develop off the east coast of Australia are a major cause of elevated coastal sea levels in this region. Their duration often exceeds a day and the combination of elevated sea levels with the high rainfall that commonly accompanies these events means that coastal flooding can be a major hazard. The processes contributing to higher-than-normal sea levels are a combination of storm surge and breaking wave setup. Three events are modelled using an atmospheric model, storm surge model and wave setup model. The storm surges resulting from the depressions are found to explain between one-third and one-half of the measured sea-level residuals at the coast and are shown to develop in a regime of coast-parallel winds that produce onshore Ekman transport. The timing of the storm surges are well captured in two of the events in which the atmospheric depressions are of broad spatial scale and well simulated by the atmospheric model. However, a poor simulation by the atmospheric model of the location of the third low, which is of smaller spatial scale, results in an inaccurate timing of the onset of the surge. The wave setup model produces sea levels at the coast that are around 11% of the incident rms wave heights. The total modelled sea-level residual, obtained by adding the modelled wave setup to the storm surge, is qualitatively similar to the measured sea-level residual. However, the modelled values are higher, especially at Sydney where the tide gauge is situated in a sheltered harbour location. In such sheltered locations, it is expected that some attenuation of the wave setup would occur and suggests that sea levels on the open coast could be considerably higher during such events.