This paper analyzes the viability of different solutions to passively augment the axial stiffness of a horizontal axis radial levitation passive magnetic bearing (PMB) with a previously studied topology. The zero-field cooling (ZFC) of high-temperature superconductor (HTS) bulks promotes higher magnetic impulsion and levitation forces and lower electromagnetic losses than those with field-cooling (FC) but, on the other hand, the guiding stability is much lower than those with FC. Because of stability reasons, FC was adopted in most superconducting maglev systems. The trend of this research group has been to develop a horizontal axis HTS ZFC radial levitation PMB presenting notable levitation forces with reduced electromagnetic losses, defined by a topology that creates guiding stability. Previous work has shown that optimizing the bearing geometry to maximize magnetic guidance forces might not be enough to guarantee the axial stiffness required for many applications. First, the extent to which guidance forces are augmented by increasing the number of HTS bulks in the stator is evaluated. Then, the axial stiffness augmentation by passively adding two limiting permanent magnet (PM) rings is evaluated. The results show that the axial stiffness is highly augmented by adding limiting PM rings with no significant additional investment. This change enables the use of the studied ZFC superconducting PMB in high-precision axial stability applications, such as precision gyroscopes, horizontal axis propellers, and turbines.