129Xe NMR measurements of adsorbed xenon are shown for the first time to be a suitable tool to characterize the porosity and the properties of the metal-organic framework Cu3(BTC)2(H2O)3 (BTC = benzene 1,3,5-tricarboxylate). The NMR experiments are performed at room temperature and over a wide range of xenon pressure and on two different synthesized Cu3(BTC)2 samples. 129Xe NMR results reveal that in dependence on the kind of the synthesis pathway either one or two signals are observed which can be attributed to two kinds of fast exchange of xenon atoms in two pores with different pore sizes. Coadsorption experiments of xenon and ethylene demonstrate that the xenon atoms prefer to fill the greater pores of the material because the smaller pores are occupied with residual molecules from the synthesis procedure and additionally adsorbed ethylene. Besides the NMR experiments a series of electron paramagnetic resonance (EPR) measurements are performed to estimate the state of copper having a strong influence on the chemical shift of the adsorbed xenon. The EPR experiments demonstrate that spin exchange between the interconnected copper dimers is taking place across the BTC linker molecules in the Cu3(BTC)2 framework.