We simulated the dynamics of azole groups (pyrazole, imidazole, 1,2,3-triazole, 1,2,4-triazole, and tetrazole) as neat liquids and tethered-via linkers to aliphatic backbones to determine how tethering and varying functional groups affect hydrogen bond networks and reorientation dynamics, both factors which are thought to influence proton conduction. We used the DL_Poly_2 molecular dynamics code with the GAFF force field to simulate tethered systems over the temperature range 200-900 K and the corresponding neat liquids under liquid state temperatures at standard pressure. We computed hydrogen bond cluster sizes; orientational order parameters; orientational correlation functions associated with functional groups, linkers, and backbones; time scales; and activation energies associated with orientational randomization. All tethered systems exhibit a liquid to glassy-solid transition upon cooling from 600 to 500 K, as evidenced by orientational order parameters and correlation functions. Tethering the azoles was generally found to produce hydrogen bond cluster sizes similar to those in untethered liquids and hydrogen bond lifetimes longer than those in liquids. The simulated rates of functional group reorientation decreased dramatically upon tethering. The activation energies associated with orientational randomization agree well with NMR data for tethered imidazole systems at lower temperatures and for tethered 1,2,3-triazole systems at both low- and high-temperature ranges. Overall, our simulations corroborate the notion that tethering functional groups dramatically slows the process of reorientation. We found a linear correlation between gas-phase hydrogen bond energies and tethered functional group reorientation barriers for all azoles except for imidazole, which acts as an outlier because of both atomic charges and molecular structure.