Recently, the concept of ordered graphs has been introduced and it was shown that isomorphism of ordered graphs can be solved in quadratic time. In the present paper we consider a special case of the subgraph isomorphism problem for ordered graphs, called marked subgraph isomorphism. An algorithm of O(m1m2) complexity is developed for finding all marked subgraph isomorphisms from a graph G1 to another graph G2, where m1 and m2 are the number of edges in G1 and G2, respectively. We demonstrate the usefulness of our algorithm by applying it to solving the subcircuit extraction problem. It turns out that our approach is much more efficient than traditional methods based on general subgraph isomorphism techniques.