In the context of monocrystalline diamond plasma deposition, the atomic hydrogen densities have been determined by two-photon absorption laser induced fluorescence in a H2/CH4 microwave plasma at high pressure (200 hPa) and high microwave power (3000 W). H-atom densities were estimated by a calibration method that consists in normalizing the H-atom TALIF intensity by the intensity from Kr atoms in a pure krypton gas at a known pressure. In the range of pressures studied, the value of the H-atom fluorescence yield, which is necessary for the calculation of absolute densities, cannot be determined experimentally, but is estimated from a model calculation that solves the rate equations describing the population changes in the various H n=3 sublevels. In plasmas containing 1% CH4, the H-atom densities reach values ≥ 1.9×1023 m-3, and the gas temperature in the plasma bulk is ~3000 K.