A clustered graph \((G,T,r)\) consists of a graph \(G=(V,E)\), a tree \(T\), and an inner vertex \(r\) of \(T\) such that the set of leaves of \(T\) is exactly \(V\). A clustered graph is said to be completely connected if every cluster, and also each complement of a cluster, induces a connected subgraph. A \(c\)-planar drawing of a clustered graph \((G,T,r)\) consists of a plane drawing of \(G\) and an inclusion representation of the rooted tree \((T,r)\) such that each edge crosses the boundary of the drawing of an inner vertex of \(T\) at most once. The authors' main result is that a completely connected clustered graph \((G,T,r)\) has a \(c\)-planar drawing if and only if \(G\) is planar. They also study the connection between the root \(r\) of \(T\) and the choice of the outer face for \(G\).