For any two given graphs, we study the problem of finding isomorphisms that correspond to inclusion-maximal common induced subgraphs that are connected. While common (induced or not) subgraphs can be easily listed using some well known reduction and state-of-the-art algorithms, they are not guaranteed to be connected. To meet the connectivity requirement, we propose an algorithm that revisits the paradigm of reverse search and guarantees polynomial time per solution (delay) and linear space, on top of showing good practical performance.