Design and optimization of cryogenic technologies for biogas upgrading require accurate determination of freeze-out boundaries. In cryogenic upgrading processes involving dry ice formation, accurate predictions of solid–liquid, solid–vapor, and solid–liquid–vapor equilibria are fundamental for a correct design of the heat exchanger surface in order to achieve the desired biomethane purity. Moreover, the liquefied biogas production process, particularly interesting for cryogenic upgrading processes due to the low temperature of the obtained biomethane, requires an accurate knowledge of carbon dioxide solubility in liquid methane to avoid solid deposition. The present work compares two different approaches for representing solid–liquid, solid–vapor, and solid–liquid–vapor equilibria for the CH4−CO2 mixture. Model parameters have been regressed in order to optimize the representation of phase equilibrium at low temperatures, with particular emphasis to the equilibria involving a solid phase. Furthermore, the extended bibliographic research allows determining the regions where more accurate data are needed.