Nanometer-thin carbon nanomembranes (CNMs) are promising candidates for efficient separation processes due to their thinness and intrinsic well-defined pore structure. This work used radioactive tracer molecules to characterize diffusion of [3H]H2O, [14C]NaHCO3, and [32P]H3PO4 through a p-[1,1',4',1″]-terphenyl-4-thiol (TPT) CNM in aqueous solution. The experimental setup consisted of two microcompartments separated by a CNM-covered micropore. Tracers were added to one compartment and their time-dependent increase in the other compartment was monitored. Occurring concentration polarization and outgassing effects were fully considered using a newly developed mathematical model. Our findings are consistent with previous gas/vapor permeation measurements. The high sensitivity toward a small molecule flow rate enables quantification of diffusion through micron-sized CNMs in aqueous solution. Furthermore, the results allow unambiguous distinction between intact and defective membranes. Even for extremely small membrane areas, this method allows detailed insight into the transmembrane transport properties, which is crucial for the design of 2D-separation membranes.