We report results from a comparative study of the influence of tail corrections on the surface tension of the Lennard-Jones fluid. We find that cutoff-independent surface tensions can be obtained by applying a set of tail corrections recently introduced by Janecek at each step of an interfacial Monte Carlo (MC) or molecular dynamics (MD) simulation. The effect of tail corrections on an alternative methodology for calculating surface tension, the combination of finite-size scaling and grand-canonical transition-matrix Monte Carlo (FSS/GC-TMMC), was also investigated. Using this indirect method, surface tensions were calculated with standard (bulk-fluid) tail corrections and lattice sums, the latter usually considered more accurate but computationally more intensive than the former. With standard tail corrections, we find that the surface tension decreases with increasing cutoff distance, reaching a limiting value corresponding to the maximum cutoff possible, namely half the simulation box length. In contrast, surface tension values obtained with the lattice summation were cutoff-independent. More importantly, these values were equivalent to those surface tension values obtained using standard tail corrections and a cutoff distance of half the box length. We also find that the surface tension values obtained here are in agreement with those found in the literature. Last, we find that surface tension values obtained by MD and FSS/GC-TMMC are in decent agreement so long as the appropriate tail correction schemes are used, and that the relative uncertainties in the surface tensions calculated by MD are generally an order of magnitude greater than those calculated by FSS/GC-TMMC. However, the time required by MD on a single central processing unit is less than that required by FSS/GC-TMMC.