This work investigates atomic recombination of gas species impinging on high-temperature materials used for thermal protection system of spacecraft entering Earth’s atmosphere. Heterogeneous catalysis models of pre-oxidized PM1000, an oxide dispersion-strengthened Ni-Cr superalloy, and silicon-carbide-coated (SiC-coated) carbon-fiber-reinforced SiC used on the European eXPErimental Re-entry Testbed (EXPERT) are fitted making use of recombination coefficients obtained experimentally from exposing these materials to highly dissociated nitrogen and oxygen flows in a plasma wind tunnel. These models are finite-rate catalytic models that consider associative adsorption, thermal desorption, and Langmuir–Hinshellwood and Eley–Rideal reactions. Recombination coefficients from different techniques are included to increase the variation of surface temperature and partial pressure of the sampling, which also increased the level of verification of the methods applied here. A pressure-dependent model for copper oxide at 320 K is also fitted, which is of special interest for investigations in ground facilities because it is commonly used as highly catalytic reference surface on plasma diagnostic probes. The materials investigated here present full surface coverage up to 1500 K at reentry relevant pressures, and the Langmuir–Hinshellwood mechanism is the dominant mechanism for a wide pressure and temperature range.