Projections of extreme sea levels (ESLs) are critical for managing coastal risks, but are made complicated by deep uncertainties. One key uncertainty is the choice of model structure used to estimate coastal hazards. Differences in model structural choices contribute to uncertainty in estimated coastal hazard, so it is important to characterize how model structural choice affects estimates of ESL. Here, we present a collection of 36 ESL data sets, from tide gauge stations along the United States East and Gulf Coasts. The data are processed using both annual block maxima and peaks-over-thresholds approaches for modeling distributions of extremes. We use these data sets to fit a suite of potentially non-stationary generalized extreme value distributions and generalized Pareto distributions by covarying the ESL statistics with multiple climate variables. For all of the sites and statistical model structures for tide surge considered here, we find that accounting for changes in the frequency of coastal extreme sea levels provides a better fit to data than using a stationary extreme value model. Further, when maximizing the a posteriori probability of the model parameters, given the available tide gauge data, generalized extreme value distribution structures with non-stationary scale parameter are preferred over non-stationary location parameter. These results have implications for how deep uncertainties in coastal flood hazards are characterized, particularly in how studies incorporate potential non-stationarity in storm surge statistics.