The number of enzymes that require a glycyl-based radical for their function is growing. Here, we provide systematic quantum-chemical studies of spin-density distributions, electronic g-tensors, and hyperfine couplings of various models of protein-bound glycyl radicals. Similarly to what is found in a companion paper on N-acetylglycyl, the small g-anisotropy for this delocalized, unsymmetrical system presents appreciable challenges to state-of-the-art computational methodology. This pertains to the quality of structure optimization, as well as to the choice of the spin-orbit Hamiltonian and the gauge origin of the magnetic vector potential. Environmental effects due to hydrogen bonding are complicated and depend in a subtle fashion on the different intramolecular hydrogen bonding for different conformations of the radical. Indeed, the conformation has the largest overall effect on the computed g-tensors (less so on the hyperfine tensors). This is discussed in the context of different g-tensors obtained by recent high-field electron paramagnetic resonance (EPR) measurements for three different enzymes. On the basis of results of a parallel calibration study for N-acetylglycyl, it is suggested that the glycyl radical observed for E. coli anaerobic RNR may have a fully extended conformation, which differs from those of the corresponding radicals in pyruvate formate-lyase or benzylsuccinate synthase.