Magnetic Resonance spectroscopy is a powerful tool for elucidating the details of molecular dynamics. In many important applications, a model of hindered diffusion is useful for summarizing the complex dynamics of ordered media, such as a liquid crystalline environment, as well as the dynamics of proteins in solution or confined to a membrane. In previous work, we have shown how the sensitivity of a magnetic resonance spectrum to the details of molecular dynamics depends on the symmetries of the magnetic tensors for the relevant interactions, e.g., Zeeman, hyperfine, or quadrupolar interactions. If the hindered diffusion is modeled as arising from an orienting potential, then the parameter sensitivity of the magnetic resonance spectrum may be studied by generalizations of methods we have introduced in previous work. In particular, we will show how lineshape calculations using eigenfunction expansions of solutions of the diffusion equation, can be used as inputs to an information-geometric approach to parameter sensitivity estimation. We illustrate our methods using model systems drawn from Nuclear Magnetic Resonance, Electron Spin Resonance, and Nuclear Quadrupole Resonance.