In the initial phase of the research process, a review of scientific literature was performed regarding the measurement uncertainty calculation methods. It is found that the most commonly used method is according to the internationally accepted document "Guide to the expression of uncertainty in measurement", i.e. GUM method. However, this method contains certain deficiencies and has been followed by the Supplement 1 which recommends using the Monte Carlo method. Furthermore, the dissertation presents the current method for determining the exchanged energy on the cross-border energy exchange as well as methods for calculation of the transmission losses. It is found that the actual methods do not involve measurement uncertainty nor systematic errors in the calculation procedure. Namely, due to large amounts of exchanged energy small percentages of systemic errors can result in significant erroneously associated energy to the transmission system operators, i.e. potential financial damage for energy exchange participants. A method for calculating the measurement uncertainty of transmission line resistance and transmission line losses using the GUM and the Monte Carlo method is developed. For the purpose of the latter method, the procedure for estimating the distribution of the output value is performed. A method for determining the measurement uncertainty of the exchange of energy and the transmission losses, including the method for correcting the exchanged energy and transmission losses for the amount of systematic errors is developed, thus reducing the total measurement uncertainty. A method for allocating the exchanged energy and the transmission losses between transmission system operators is developed as well. Practical results show that the measurement uncertainty is reduced after correcting systematic errors, thus confirming the hypothesis of the dissertation. It can be concluded that this method represents a fairer way to determine the exchanged energy and the transmission losses on the cross-border energy exchange.