  We provide a direct method for proving Craig interpolation for a range of
modal and intuitionistic logics, including those containing a "converse"
modality. We demonstrate this method for classical tense logic, its extensions
with path axioms, and for bi-intuitionistic logic. These logics do not have
straightforward formalisations in the traditional Gentzen-style sequent
calculus, but have all been shown to have cut-free nested sequent calculi. The
proof of the interpolation theorem uses these calculi and is purely syntactic,
without resorting to embeddings, semantic arguments, or interpreted connectives
external to the underlying logical language. A novel feature of our proof
includes an orthogonality condition for defining duality between interpolants.
