In a recent paper, we described similarities between the superionic transition in certain crystals and the glass transition in fragile, supercooled liquids. We now examine the underlying energy landscapes of the fluorides of lead(II) and calcium, by minimizing the potential energy from configurations along molecular-dynamics trajectories. The resulting inherent structures are characterized by the number of defects they contain and the interactions of these defects. We propose a simple explanation for the clustering of these defects, related to the lattice's strain energy, and discuss its implications for the mechanism of conduction. We also consider the vibrational densities of states of the inherent structures and test the possibility that an increase in the harmonic vibrational entropy upon defect formation stabilizes the superionic state. A mean-field model with an interaction term varying with the cube-root of the defect concentration describes the inherent structure defect populations well, and also reproduces the energy and entropy over a significant temperature range. However, a direct examination of the way in which the inherent structure energy depends on the defect concentration shows that this does not mean that the physical picture used to construct the mean-field free energy is correct.