Sea-level rise is a key driver of projected flooding risks. The design of strategies to manage these risks often hinges on projections that inform decision-makers about the surrounding uncertainties. Producing semi-empirical sea-level projections is difficult, for example, due to the complexity of the error structure of the observations, such as time-varying (heteroskedastic) observation errors and autocorrelation of the data-model residuals. This raises the question of how neglecting the error structure impacts hindcasts and projections. Here, we quantify this effect on sea-level projections and parameter distributions by using a simple semi-empirical sea-level model. Specifically, we compare three model-fitting methods: a frequentist bootstrap as well as a Bayesian inversion with and without considering heteroskedastic residuals. All methods produce comparable hindcasts, but the parametric distributions and projections differ considerably based on methodological choices. Our results show that the differences based on the methodological choices are enhanced in the upper tail projections. For example, the Bayesian inversion accounting for heteroskedasticity increases the sea-level anomaly with a 1% probability of being equaled or exceeded in the year 2050 by about 34% and about 40% in the year 2100 compared to a frequentist bootstrap. These results indicate that neglecting known properties of the observation errors and the data-model residuals can lead to low-biased sea-level projections.