Stricter requirements from the European Union and the German government regarding the utilization of renewable and sustainable fuels for transportation, power, and heat production are currently in effect. This has led to that heavy transportation companies are looking for a more sustainable alternative to liquefied natural gas, such as liquefied biomethane. The monetary costs for the release of greenhouse gas are also increasing due to the carbon certificates that are being traded are decreasing in numbers each year. Carbon certificates grant companies an allowance of releasing a certain amount of emissions without being fined. Carbon dioxide and biomethane liquefaction can be a good investment for producers of biomethane to find new markets by for example trading in carbon certificates, selling liquid carbon dioxide, and producing liquefied biomethane as an alternative transportation fuel. The sale price of biomethane is heavily dependant on the emission factor for the biomethane and as such, capturing the carbon dioxide from the biomethane plant and off-setting fossil carbon dioxide would increase the sale price of the biomethane. The methods used are theoretical and quantitative, Numerical data was collected to be able to perform the economical and environmental calculations. The investment cost for the liquefaction technologies was scaled down to correspond to a plant with a production capacity of 350 Nm3/h. Also included in this thesis is a review of biomethane production, together with theory for the economical and environmental calculations.  By performing a technical, economical and environmental assessment of the technologies for the liquefaction of carbon dioxide and biomethane. This thesis shows that liquefaction of biomethane is not an economical viable option at the moment for plants equal or below this production capacity, due to a negative net present value, negative return on investment, sensitivity to fluctuating costs, and a high payback time. However, it could help in achieving the sustainability goals set forth by the European Union and the German government. With regards to the liquefaction of carbon dioxide it is deemed a viable investment option with an investment cost of approximately 1 million Euro and a payback time of approximately 3 years. Liquefaction of carbon dioxide could bring an extra income to the biomethane plant. This due to an added revenue in the sales of liquid carbon dioxide and an increase in the sale price of biomethane due to a reduction of the emission factor from 17 gCO2-eq /MJ to -23 gCO2-eq /MJ. The investment could also help achieving the sustainability goals by decreasing the dependence on fossil carbon dioxide for various sectors.