A fast-field-cycling NMR investigation was carried out on a set of polyurethane cyclodextrin nanosponges, in order to gain information on their textural properties, which have been proven to be quite difficult to assess by means of ordinary porosimetric techniques. Experiments were performed on both dry and wet samples, in order to evaluate the behavior of the "nonexchangeable" C-bound H-1 nuclei, as well as the one of the mobile protons belonging to the skeletal hydroxyl groups and the water molecules. The results acquired for the wet samples accounted for the molecular mobility of water molecules within the channels of the nanosponge network, leading back to the possible pore size distribution. Owing to the intrinsic difficulties involved in a quantitative assessment of the textural properties, in the present study we alternatively propose an extension to nanosponges of the concept of "connectivity", which has been already employed to discuss the properties of soils.