Predictions of sea level changes over the forthcoming decades contain irreducible uncertainties due to internal climate variability. These uncertainties are commonly estimated from spread of sea level predictions obtained in Global Climate Models (GCM) under the same forcing but with slightly different initial conditions. In this study, we focus on an internal climate variability metric based on the analysis of temporal behavior of sea level time series. We analyze sea level variations simulated by Community Climate System Model version 4 (NCAR-CCSM4) and Community Earth System Model version 1 (CESM 1). We demonstrate the persistence of sea level variations over decadal - interdecadal scales in the extratropical and polar regions and highlight its importance for the long-term predictions. Comparison of the sea level persistence simulated by the models with a set of century-long tidal records shows a general agreement with some exceptions due, probably, to a yet limited spatial resolution of the GCMs. The impact of the persistence (often known as long-term memory) is converted to irreducable incertainties in the sea level changes. These intrinsic uncertainties in the future sea level changes are shown to be strongly enhanced in some regions (e.g. North Atlantic, North Pacific, Polar regions) and should be taken into account in sea level predictions.