An orientable relative embedding of a graph is an embedding for which some of the face boundaries have been prespecified. Thus, given some closed walks \(W_ 1,\dots,W_ k\) of the graph \(G\), one might ask questions about the set of all the orientable embeddings in which these walks bound some faces. The authors’ main result proves an analog of Duke’s interpolation theorem for relative embeddings. They also obtain some partial results on the relative maximum genus of some regular graphs.