This paper presents the first steps toward a graph comparison method based on matching matchings, or in other words, comparison of independent edge sets in graphs. The novelty of our approach is to use matchings for calculating distance of graphs in case of edge-colored graphs. This idea can be used as a preprocessing step of graph querying applications, to speed up exact and inexact graph matching methods. We introduce the notion of colored matchings and prove some properties of them in edge colored complete graphs and complete bipartite graphs in case of two colors.