Single-ion magnets based on lanthanide ions in pseudo-D5h symmetry have gained much attention in recent years as they are reported to possess a large blocking temperature and a large barrier for magnetization reversal. Magneto-structural correlations reveal that the axial O-Ln-O angle is an important parameter to control the barrier, and while it can be fine-tuned by chemical modification, an alternative would be to utilize hydrostatic pressure. Herein, we report the crystal structures and static magnetic properties of two air-stable isostructural lanthanide SIMs under applied pressures. The complexes exhibit pseudo-D5h symmetry around the Ln(III)-ion (Ln = Dy or Ho), which coordinates to five equatorial water molecules and two large neutral phosphonic diamide ligands along the axial direction. High-pressure single-crystal X-ray diffraction experiments revealed two phase-transitions and an increasing deviation from D5h-symmetry between ambient pressure and 3.6 GPa. High-pressure direct-current magnetic measurements of the Dy(III) compound showed large steps in the hysteresis loops near zero field, indicative of quantum tunneling of magnetization (QTM). These steps grow in size with increasing pressure, suggesting that QTM becomes progressively more active, which correlates well with the pressure-induced increased overall deviation from pseudo-D5h symmetry and decreasing axial O-Dy-O angle. A strong temperature dependence of the step size is seen at 0.3 GPa, which shows that the SMM character persists even at this pressure. To understand the origin of significant variation in the tunneling probability upon pressure, we performed a range of ab initio calculations based on the CASSCF/RASSI-SO/SINGLE_ANISO method on both Dy and Ho complexes. From the energies and magnetic anisotropy of the mJ sublevels, we find a complex variation of the energy barrier with pressure, and using a constructed geometrical parameter, R, taking into account changes in both bond angles and distances, we link the magnetic properties to the first coordination sphere of the molecules.