The El Niño-Southern Oscillation (ENSO) is the dominant mode of year-to-year climate fluctuations with wide-ranging socio-economic and environmental impacts. Understanding its response to a warmer climate is paramount, but the role of internal climate variability in modulating the response is not clear. Using 40 Community Earth System Model Large Ensemble (CESM-LE) simulations and 47 Max Planck Institute for Meteorology Grand Ensemble (MPI-GE) members, we find that internal variability generates a spread in ENSO standard deviation and skewness that is similar to the spread of 17 selected Coupled Model Intercomparison Project phase 5 (CMIP5) models. Based on CESM-LE and MPI-GE, internal variability can explain between 90 to 100% of the ENSO standard deviation and all (100%) of the ENSO skewness spread in the 17 CMIP5 models. Both CESM-LE and the selected CMIP5 models project that the standard deviation of eastern and central Pacific ENSO will increase in a warmer climate. However, MPI-GE shows no agreement, highlighting that different models have a different response of ENSO to a warmer climate and that there is large uncertainty within the CMIP5 ensemble which may be caused by internal climate variability.