As a complement to measurements, numerical modeling facilitates improved understanding of the complex turbulent processes in the stratocumulus-topped boundary layer (STBL). Due to limited computational resources simulations are often run at too coarse resolutions to resolve details of cloud-top turbulence and potentially in computational domains too small to account for the largest scales of boundary layer circulations. The effects of such deficiencies are not fully understood. Here the influence of resolution/anisotropy of the computational grid and domain size in under-resolved implicit large-eddy simulation of the STBL is investigated. The performed simulations are based on data from the first research flight of the DYCOMS-II campaign. Regarding cloud cover and domain-averaged liquid water path, simulations with horizontal/vertical grid spacing of 35/5 m, 70/10 m, and 105/15 m are found to agree better with measurements than more computationally expensive simulations with isotropic grid boxes, e.g., with 10/10 m or 15/15 m grid spacing. While decreasing the vertical grid spacing allows more representative simulation of the thin, turbulent, stably stratified interfacial layer between the STBL and the free troposphere, coarsening the horizontal resolution dampens vertical velocity fluctuations in this region and mimics the observed anisotropy of stably stratified small-scale turbulence near the cloud top. The size of the computational domain is found to have almost no impact on mean cloud properties. However, increasing it from math formula to math formula does lead to the occurrence of larger coherent updraft structures. Increasing it further to math formula shows little or no increase in the updraft size.