Methane is a promising propellant for future liquid rocket engines. In the cooling channels of a regeneratively cooled engine, it would be close to the critical point. This results in drastic changes in the fluid properties, which makes cooling analysis a challenge. This thesis describes a two-pronged approach to tackle this problem. Simple and fast engineering tools allow for the development of insight in the design space using rapid iterations and parametric analyses. However, they are often rather inaccurate. In contrast, detailed multi-dimensional tools for numerical analysis are more accurate, but they require more computation time. Both approaches are developed for the analysis of regenerative cooling channels of oxygen/methane engines. Each approach uses complex but accurate models for the thermodynamic and transport properties of methane. OMECA (short for One-dimensional Methane Engine Cooling Analysis) is a one-dimensional tool that was developed in Python from scratch. This tool divides a nozzle into stations and analyses the one-dimensional thermal equilibrium at each station. It makes extensive use of semi-empirical equations to calculate the heat transfer at both the hot gas side and the coolant side. The tool is compared to a coupled multi-physics analysis tool, showing that the accuracy of the wall temperature is rather poor, with discrepancies of up to 150~K. Both at the hot gas and coolant side, large deviations are present. However, if the input heat flux is correct, OMECA predicts the coolant pressure drop and temperature rise with a 10% accuracy. To obtain a higher accuracy at the coolant side, the open-source CFD package OpenFOAM is adapted for analysis of supercritical methane. Of particular note is the custom library that interpolates the fluid property tables at runtime. The selected solver is applicable to steady-state compressible flows. The software is then systematically validated using three validation cases. With experimental validation data obtained through cooperation with CIRA, an accuracy of 15 K for the wall temperature prediction is demonstrated. The pressure drop is predicted within 10%. Traditionally, the launcher industry uses copper alloys as wall material in regeneratively cooled combustion chambers. They offer a high allowable temperature and high thermal conductivity, but are also heavy and expensive. Recently, several companies have demonstrated aluminium combustion chambers. Aluminium alloys have weight and cost advantages, but have lower allowable temperature and thermal conductivity. The developed tools for cooling analysis are therefore employed to compare aluminium and copper for a generic 10~kN combustion chamber. It is discovered that a thermal barrier coating must be employed to protect the hot gas side of an aluminium combustion chamber, otherwise regenerative cooling is not feasible. Even with such a coating, the pressure drop required to cool the coated aluminium chamber is three times higher than the pressure drop required for a copper chamber. A difference in pressure drop has effects on the vehicle level. A larger pressure drop in the cooling channel of a rocket engine necessitates a higher feed pressure. For a pressure fed engine, this means the tank must be stronger and heavier. It is found that even at modest fuel mass, the increase in tank mass is eight times as large as the decrease in engine mass offered by aluminium. This shows that using aluminium for the chamber wall is not advantageous with respect to copper for a pressure fed, regeneratively cooled, oxygen/methane rocket engine.