This data set contains model output of idealized, 400 years long, simulations conducted with the Norwegian Earth System Model NorESM2-LM. NorESM2 is described in Seland et al. (2020) and Tjiputra et al. (2020). It comprises 10 different simulations, 7 of which have 3 ensemble members, and a control run. 4 of the simulations follow the ZECMIP protocol (Jones et al. 2019), i.e., there are CO2 emissions following a bell-shaped emission curve in the first 100 years and zero emissions thereafter (we have simulated 300 years of zero emissions). The total carbon emissions in these simulations are 1500, 1750, 2000, and 2500 Pg C, and we refer to these simulations as "esm-bell-xxxxPgC" or shorter "Bxxxx", where xxxx is the amount of carbon emissions. The B1500 simulation serves as a reference simulation reaching approximately 1.7 degrees in the long term. From the B1750 to B2500 simulations we have branched off 6 simulations with negative emissions to simulate "overshoots" of different length and duration. We apply negative emission of 250, 500, and 1000 Pg cumulative carbon removal over a time span of 100 years. At the end of the negative emission phases all simulations have experienced the same amount of cumulative carbon emissions as the reference simulation (1500 Pg C). To simulate overshoots of different duration, we vary the branch point in time such that there are either 0 or 100 years of zero emissions before CDR is applied. The overshoot simulations are referred to as, for example, "esm-brch-bell-1750PgC-000y-cdr0250PgC" for the overshoot that is branched from the esm-bell-1750PgC simulation 0 years after positive emissions cease with a total of 250 Pg C CDR applied. All simulations are CO2-emission driven, and CO2 is the only variation in forcing that is applied. Land use and non-CO2 forcings are kept constant at pre-industrial levels. The raw model output has been processed with the "Climate Model Output Rewriter" (it has been "cmorized") and is compliant with CMIP6 model output and metadata requirements. The simulations and model output are described in more detail in the enclosed file README-NorESM2_Idealized_overshoots_technical_description_NIRD.pdf