An intercomparison between 10 single-column (SCM) and 5 large-eddy simulation (LES) models is presented for a radiation fog case study inspired by the Local and Non-local Fog Experiment (LANFEX) field campaign. Seven of the SCMs represent single-column equivalents of operational numerical weather prediction (NWP) models, whilst three are research-grade SCMs designed for fog simulation, and the LESs are designed to reproduce in the best manner currently possible the underlying physical processes governing fog formation. The LES model results are of variable quality and do not provide a consistent baseline against which to compare the NWP models, particularly under high aerosol or cloud droplet number concentration (CDNC) conditions. The main SCM bias appears to be toward the overdevelopment of fog, i.e. fog which is too thick, although the inter-model variability is large. In reality there is a subtle balance between water lost to the surface and water condensed into fog, and the ability of a model to accurately simulate this process strongly determines the quality of its forecast. Some NWP SCMs do not represent fundamental components of this process (e.g. cloud droplet sedimentation) and therefore are naturally hampered in their ability to deliver accurate simulations. Finally, we show that modelled fog development is as sensitive to the shape of the cloud droplet size distribution, a rarely studied or modified part of the microphysical parameterisation, as it is to the underlying aerosol or CDNC.