The current uncertainty surrounding the Earth's equilibrium climate sensitivity is an important driver for climate hazard projections. While the implications for projected global temperature changes have been extensively studied, the impacts on sea level projections have been relatively unexplored. Here we analyze the relationship between the climate sensitivity and sea level projections, with a particular focus on the high‐impact upper tail. We utilize a Bayesian calibration of key climate and sea level parameters using historical observations and the reduced‐complexity Earth system model, Hector‐BRICK. This methodology allows us to focus on plausible realizations of the climate system in a probabilistic framework. We analyze the effects of high‐end climate sensitivity (above 5 K) on projections and spatial patterns of sea level change. The sea level projections hinge critically on the upper tail of the climate sensitivity, especially for the highly decision‐relevant upper tail. Results have important implications for timing of threshold exceedances and regional variability. Plain Language Summary The upper tail of sea level rise over the coming century can be an important factor for adaptation planning and the assessment of vulnerabilities and risks. One way to estimate this upper tail is with a simple climate model, which can provide useful constraints on sea level rise informed by historical observations. The model range reflects uncertainty about the evolution of the climate system and physical processes related to sea level, such as melting land ice. Here we investigate the effect of a key climate uncertainty, Earth's long‐term temperature response to a doubling of atmospheric CO2, on the model range of 21st century sea level rise, using the simple climate model Hector‐BRICK. While all of the model realizations generally match historical observations, those with a high temperature sensitivity to atmospheric CO2 have generally higher 21st century sea level rise. We explore the time evolution of this effect and focus on the particularly large change in the upper tail of sea level. Key Points We analyze the effect of high climate sensitivity on sea level rise projections using a reduced‐complexity Earth system model, Hector‐BRICK Modeled sea level projections, particularly at the upper tail, depend substantially on equilibrium climate sensitivity Results influence regional sea level change projections and the timing of sea level rise exceedances