Pressure metrology in cryogenic ultrahigh vacuum is limited by the need for in situ readout that does not perturb the cold environment. We propose a passive gauge based on the vertical translational mode of a ferromagnetic sphere levitated above a superconducting surface by the Meissner effect. In the molecular-flow regime, gas-surface momentum exchange adds a damping rate ${\gamma }_{\mathrm{gas}}\propto P$, so the pressure can be inferred from mechanical ring-down. Using Fisher-information analysis, we derive Cramér–Rao lower bounds for estimating the total damping rate and propagate them to an analytic pressure uncertainty that includes pressure-independent losses from residual dissipation and eddy currents. The resulting scalings with sphere radius $R$ reveal an optimum: larger $R$ improves low-$P$ sensitivity but increases intrinsic damping and narrows the molecular-flow range. For $T_{\mathrm{env}}=4.2\mathrm{K}$ and intrinsic damping ${\gamma }_0={10}^{-6}{\mathrm{s}}^{-1}$, we find $R_{\mathrm{opt}}\approx 2.4\mathrm{mm}$ and a resolution floor $\delta P_{\text{mea}}\approx 4\times {10}^{-10}\mathrm{Pa}$ at a signal-to-noise ratio of 1, with a molecular-flow upper limit of ${10}^{-2}–{10}^{-1}\mathrm{Pa}$ set by gas species and the Knudsen criterion. These results provide sizing and integration-time guidelines for levitated mechanical cryogenic vacuum gauges.

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• Cryogenics & vacuum technology
• Low Reynolds number flows
• Meissner effect
• Metrology
• Ultracold gases
• Pressure techniques