Estimating the magnitude of sea level rise (SLR) for the end of 21st century is among the primary goals of current climate research. An important practical aspect of this problem is that any projection of the SLR is obtained with uncertainty, which is partly due to internal variability of the Earth climate system. This internal variability is due to complex non-linear interactions within the Earth climate system and can induce diverse quasi-periodic oscillatory modes and a long-term memory behavior. It has been demonstrated that the interplay of long-term memory fluctuations in sea level changes can be modeled by a power-law process. Therefore, this makes possible the uncertainty estimations in sea level trends caused by the internal variability. The obvious question is whether the long-memory of the internal variability is correctly simulated in climate models. In this study, we (1) analyze the scaling behaviour of the sea level fluctuations projected for the 21st century by the National Center for Atmospheric Research Community Climate System Model (NCAR-CCSM) and (2) compare the uncertainties in predicated sea level changes obtained from a NCAR-CCSM multi-member ensemble simulations with estimates derived from the Lennartz-Bunde statistics for the power-law processes.