Simulations of the CMIP6 historical period 1850–2014, characterized by the emergence of anthropogenic climate drivers like greenhouse gases, are presented for different configurations of the NASA Goddard Institute for Space Studies (GISS) Earth System ModelE2.1. The GISS‐E2.1 ensembles are more sensitive to greenhouse gas forcing than their CMIP5 predecessors (GISS‐E2) but warm less during recent decades due to a forcing reduction that is attributed to greater longwave opacity in the GISS‐E2.1 pre‐industrial simulations. This results in an atmosphere less sensitive to increases in opacity from rising greenhouse gas concentrations, demonstrating the importance of the base climatology to forcing and forced climate trends. Most model versions match observed temperature trends since 1979 from the ocean to the stratosphere. The choice of ocean model is important to the transient climate response, as found previously in CMIP5 GISS‐E2: the model that more efficiently exports heat to the deep ocean shows a smaller rise in tropospheric temperature. Model sea level rise over the historical period is traced to excessive drawdown of aquifers to meet irrigation demand with a smaller contribution from thermal expansion. This shows how fully coupled models can provide indirect observational constraints upon forcing, in this case, constraining irrigation rates with observed sea level changes. The overall agreement of GISS‐E2.1 with observed trends is familiar from evaluation of its predecessors, as is the conclusion that these trends are almost entirely anthropogenic in origin.