  We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on
a compact Riemannian manifold with smooth boundary. This problem is a natural
generalization of the classical Steklov problem on functions. We derive a
number of upper and lower bounds for the first eigenvalue in several contexts:
many of these estimates will be sharp, and for some of them we characterize
equality. We also relate these new eigenvalues with those of other operators,
like the Hodge Laplacian or the biharmonic Steklov operator.
