Monte Carlo simulations have been used to calculate the surface tension of a planar liquid-vapor interface of a Lennard-Jones fluid using a new cylindrical truncation correction procedure. A bubble was mimicked by simulating a Lennard-Jones liquid close to coexistence containing a single immobile hard-sphere cavity. From the density profile of this system the curvature dependent surface tension has been estimated via calculation of the Helmholtz free energy of the system and separately using a large cavity contact density expansion. Evidence is presented that the Tolman length becomes increasingly negative as the critical temperature is approached and possibly changes sign.