Long channels with diameter of few tens of nanometer are produced by chemical track etching of swift heavy ion irradiated muscovite sheets. Such small apertures are most suitable e.g. as beam defining apertures for focusing systems in ion beam facilities enabling beam diameters down to a few nanometers. One of the most important parameters to consider is the interaction of the ion beam with the walls of the aperture. We report angle-resolved transmission and energy-loss measurements of MeV ion beams through ion-track-etched capillaries with very high aspect ratio of about 60. For all ion energies, the angle-resolved transmission curves measured through the channels show a significant enhancement with respect to the expected pure geometrical considerations. This broadening of the acceptance angle increases further when the kinetic energy is reduced. This effect is ascribed to low-angle scattering of the ions at the surface of the muscovite capillary walls. These results are well described by simulations applying a similar approach as used for ion beam channeling in crystals.