Small molecules serve as valuable benchmarks for testing quantum chemical theories. Ultra-high-resolution spectroscopy currently offers the capability of measuring molecular hydrogen energy levels with a relative accuracy on the order of 10-10. Expanding such investigations to encompass different isotopologues of molecular hydrogen has emerged as a promising avenue for examining mass-dependent contributions to the full description of molecular structure in the framework of relativistic quantum electrodynamics. However, the delicate nature of handling radioactive tritium in a high-resolution spectroscopy environment poses significant technological challenges, thereby limiting the extension of these studies to include T2, DT and HT isotopologues. In this work, we present the experimental setup of the very sensitive, Doppler-free technique of Noise-Immune Cavity-Enhanced Optical Heterodyne Molecular Spectroscopy (NICE-OHMS), used to measure rovibrational transitions in the HT molecule. The NICE-OHMS measurements were performed in a closed cavity system without connection to an actively pumped vacuum system. For this reason, a new method for tritium storage and pressure regulation within 0.05–1Pa based on a temperature-controlled mini-getter system is employed using less activity than the tritium exemption limit (1GBq). Non-Evaporable Getters of the type SAES St171 were used for this purpose exploiting their property that hydrogen is released upon heating, while other gases remain being pumped. Prior to the NICE-OHMS experiment, the reversible sorption properties of the getter for hydrogen isotopes were investigated. We show measurements of the equilibrium (hydrogen) pressure for all three pure isotopes and for a H2:HT:T2 mixture (with H:T = 1:1) as a function of temperature for a system of defined volume and amount of gas. For the read-out of the temperature, a method using the resistance of the getter in combination with a pyrometric calibration has been implemented. We discuss the experiences from practical use of the tritium getter and show results obtained with the NICE-OHMS setup leading to frequency calibration of near-infrared transitions in HT at an accuracy, surpassing previous studies by nearly three orders of magnitude.