Climate models struggle to accurately represent the highly reflective boundary layer clouds overlying the remote and stormy Southern Ocean. We use in situ aircraft observations from the Southern Ocean Clouds, Radiation and Aerosol Transport Experimental Study (SOCRATES) to evaluate Southern Ocean clouds in a cloud‐resolving large‐eddy simulation (LES) and two coarse resolution global atmospheric models, the CESM Community Atmosphere Model (CAM6) and the GFDL Atmosphere Model (AM4), run in a nudged hindcast framework. We develop six case studies from SOCRATES data which span the range of observed cloud and boundary layer properties. For each case, the LES is run once forced purely using reanalysis data (fifth generation European Centre for Medium‐Range Weather Forecasts atmospheric reanalysis, “ERA5 based”) and once strongly nudged to an aircraft profile(“Obs based”). The ERA5‐based LES can be compared with the global models, which are also nudged to reanalysis data and are better for simulating cumulus. The Obs‐based LES closely matches an observed cloud profile and is useful for microphysical comparisons and sensitivity tests and simulating multilayer stratiform clouds. We use two‐moment Morrison microphysics in the LES and find that it simulates too few frozen particles in clouds occurring within the Hallett‐Mossop temperature range. We tweak the Hallett‐Mossop parameterization so that it activates within boundary layer clouds, and we achieve better agreement between observed and simulated microphysics. The nudged global climate models (GCMs) simulate liquid‐dominated mixed‐phase clouds in the stratiform cases but excessively glaciate cumulus clouds. Both GCMs struggle to represent two‐layer clouds, and CAM6 has low droplet concentrations in all cases and underpredicts stratiform cloud‐driven turbulence.