Emerging high-resolution global ocean climate models are expected to improve both hindcasts and forecasts of coastal sea level variability by better resolving ocean turbulence and other small-scale phenomena. To examine this hypothesis, we compare annual to multidecadal coastal sea level variability over the 1993-2018 period, as observed by tide gauges and as simulated by two identically-forced ocean models, at $\sim$1$^{\circ}$ (LR) and $\sim$0.1$^{\circ}$ (HR) horizontal resolution. Differences between HR and LR, and misfits with tide gauges, are spatially coherent at regional alongcoast scales. Resolution-related improvements are largest in, and near, marginal seas. Near attached western boundary currents, sea level variance is several times greater in HR than LR, but correlations with observations may be reduced, due to intrinsic ocean variability. Globally, in HR simulations, intrinsic variability comprises from zero to over 80\% of coastal sea level variance. Outside of eddy-rich regions, simulated coastal sea level variability is generally damped relative to observations. We hypothesize that weak coastal variability is related to large-scale, remotely-forced, variability; in both HR and LR, tropical sea level variance is underestimated by $\sim$50\% relative to satellite altimetric observations. Similar coastal dynamical regimes (e.g., attached western boundary currents) exhibit a consistent sensitivity to horizontal resolution, suggesting that these findings are generalizable to regions with limited coastal observations.