Despite the fact that the surface tension for a Lennard-Jones fluid has been simulated many times in the past, there is some considerable disagreement between the results. This paper calculates the surface tension and density profiles for the liquid-vapour interface of a Lennard-Jones fluid using molecular dynamics (MD) simulation techniques for a variety of system sizes, film thicknesses, interfacial areas, interatomic potential cut-offs, and temperatures. The results are compared with previous work in order to resolve some of the discrepancies of the past work. Combining this work with some reliable results from the past, the minimum system size, film thickness, and equilibration time necessary for the accurate description of the surface tension was determined. Using simulation results calculated for computationally-economic values of the potential cut-off, the surface tension was extrapolated to the full potential value using a tail correction and the results compared to simulations performed with longer cut-offs. The results indicated the possibility of obtaining estimates of the surface tension for models employing a large cut-off from those with a more moderate cut-off value. The criteria established for obtaining accurate results for the pure components was applied to binary mixtures of Lennard-Jones particles approximating mixtures of argon and krypton. The preferential adsorption at the interface was examined, the tail correction was applied to the mixtures, and the ‘corrected’ surface tensions compared to experimental results.