A new method has been developed to determine the surface anchoring strengthWand the tilt &thgr;tof the nematic director from the normal to a curved nematic–air interface. This method is based on the comparison of interference textures obtained by polarization microscopy experiments to numerical simulations of nematic liquid crystals within partially filled cylindrical tubes enforcing homeotropic anchoring. For the nematic liquid-crystal mixture ZLI 2860, we obtain &thgr;t=7°±1°,W=(1.5±0.5)×10−6J/m2at the nematic–tube andW>10−5J/m2at the nematic–air interface. ©1997 American Institute of Physics.