The controlled shaping and surface functionalization of colloidal particles has provided opportunities for the development of new materials and responsive particles. The possibility of creating hollow particles with semipermeable walls allows modulating molecular transport properties on colloidal length scales. While shapes and sizes can typically be observed by optical means, the underlying chemical and physical properties are often invisible. Here, we present measurements of cross-membrane transport via pulsed field gradient NMR in packings of hollow colloidal particles. The work is conducted using a systematic selection of particle sizes, wall permeabilities, and osmotic pressures and allows tracking organic molecules as well as ions. It is also shown that, while direct transport of molecules can be measured, indirect markers can be obtained for invisible species via the osmotic pressure as well. The cross-membrane transport information is important for applications in nanoconfinement, nanofiltration, nanodelivery, or nanoreactor devices.