We study the surface tension for thin, amorphous polymer films by means of computer simulation. Using molecular dynamics, we present surface tension measurements via the fluctuation spectrum of capillary waves in the long-wavelength limit for sufficiently large systems. We find good agreement with a theory based on continuum mechanics. In addition, we observe the spreading of the surface thickness with increasing lateral system size, an effect which allows another estimate of the surface tension. Furthermore, we studied the correlation between two surfaces and measured the transverse length scale by varying the him thickness. We also present data of the temperature dependence of the bulk density of the polymer film and the thickness of the surface region in the regime above the glass transition temperature.