C-13-NMR measurements of the chiral mesogen cholesteryl-undecylcarbonate (CHUC) adsorbed in Anopore membranes with cylindrical pores of 0.2 mu m diameter are presented. The pitch of CHUC in the cholesteric phase is of order of the pore diameter, and in view of the planar axial anchoring a strong in fluence of the walls on the director field can be expected. Simulation of the angular dependence of C-13-NMR line shape allows to determine a mean tilt angle of 60 degrees of the director with respect to the helical axes which are oriented along the channels. Furthermore, at T=341K a correlation time of 130 mu s for reorientational motions could be obtained which is connected with molecular diffusion along the pores. Optical and NMR-measurements are compatible with a tilted helical director field for the cholesteric LC material within the pores.