In addition to their importance as abundant hydrocarbon deposits in nature, clathrate hydrates are being studied as potential media for hydrogen and carbon dioxide storage and as "nano-reactors" for small molecules. However, little is known about the behavior of reactive species in such materials. We have employed muon spin spectroscopy to characterize various organic free radicals that reside as isolated guests in structure II clathrates. The radicals are formed by reaction of atomic muonium (Mu) with the guest molecules furan and two isomeric dihydrofurans. Muonium is essentially a light isotope of hydrogen and adds to unsaturated molecules in the same manner as H. We have determined muon and proton hyperfine coupling constants for the muoniated radicals formed in the clathrates and also in neat liquids at the same temperature. DFT calculations were used to guide the spectral assignments and distinguish between competing radical products for Mu addition to furan and 2,3-dihydrofuran. Relative signal amplitudes provide yields and thus the relative reactivities of the C4 and C5 addition sites in these molecules. Spectral, features, hyperfine constants, and reactivities all indicate that the radicals do not tumble freely in the clathrate cages in the same way that they do in liquids.