We study the surface properties of a molecular model of a liquid crystal using a density functional theory. The intermolecular interaction includes a Maier-Saupe term as well as terms which break the orientational symmetry at the interface. These latter contributions prove to play an essential role in the explanation of some of the anomalous surface-tension features observed in experimental systems. In particular, a dramatic surface tension maximum above the clearing point T-NI is Seen to be associated with increased nematic order close to the nematic-vapor interface. In addition, further reduction of the surface tension with decreasing temperature below T-NI is observed to be related either with rapidly increasing surface-enhanced order, in which case there is a surface tension minimum, or with growing surface smectic order above the nematic-smectic transition temperature.