The infrared gas-phase absorption spectrum of methane was used to determine its Clapeyron solid-gas equilibrium curve in the 40-77 K temperature range. For comparative purposes and to obtain more reliable results, two different optical experimental setups were used. At higher temperatures (53-77 K), a single pass cryogenically cooled cell was coupled to a standard low-resolution Fourier transform infrared spectrometer. The second system was a state-of-the-art vertical-external-cavity surface-emitting laser tunable source operating at around 2.3 mu m, combined with a 7 m path Herriott cell, to record methane absorption features down to 40 K. From the measurements, the vapor pressure curve In(p/Pa) = -(1191.92 +/- 8.92)/(T/K) + (22.49 +/- 0.16) was derived in the range 40-77 K. This corresponds to a value of 9910 +/- 75 J mol(-1) for the sublimation enthalpy. The relation was validated down to 40 K, increasing our knowledge of the saturation pressure by 2 orders of magnitude. Data were compared with available pressure measurements from the literature, obtained by manometric or mass spectrometry techniques, and the sublimation enthalpy was compared with a thermodynamic approach based on heat capacity measurements in the solid and gas phases.