Topics related to sustainable economic development are currently important issues in the modern world. However, the implementation of this concept and related operational strategies raises many controversies. On the one hand, it offers hope for ecological, safe, and independent economic development, while on the other hand, it raises public concerns about the costs of such changes. These problems are widely appreciated in the EU, which is the undoubted leader in implementing the concept of sustainable economic development. With regard to this issue, this paper presents the developed methodology for assessing the sustainable energy and climate development of the EU-27 countries. The basis of this assessment is 17 selected indicators characterizing the most important areas related to this development. Their selection was conditioned by the assumptions of the Europe 2020 Strategy and the goals (7 and 13) of the UN Agenda for Sustainable Development 2030. Five widely used methods for multi-criteria analysis supporting management processes (CODAS, EDAS, TOPSIS, VIKOR, and WASPAS) were used for the study. In order to carry out an unambiguous assessment and determine the final ranking of countries in terms of energy and climate sustainability, a methodology was developed to specify the normalized value of the Final Assessment Score (Asfinal). Based on it, the sustainability of individual EU-27 countries in 2010, 2015, and 2020 was assessed, and this assessment formed the basis for dividing these countries into four classes (levels) in terms of sustainability. The results confirmed the high differentiation of the EU-27 countries in terms of sustainability, indicating leaders as well as countries with low levels of sustainability. The countries with the highest and most stable levels of sustainable development of the economy are Sweden and Denmark. The results provide opportunities for their interpretation, both in terms of analyzing changes in individual indicators and in terms of the global assessment of sustainable development in individual countries. These results should be used when developing an energy and climate strategy for the next few years for the EU as a whole and for individual countries.