  We discuss the Renyi entanglement entropies of descendant states in critical
one-dimensional systems with boundaries, that map to boundary conformal field
theories in the scaling limit. We unify the previous conformal-field-theory
approaches to describe primary and descendant states in systems with both open
and closed boundaries. We provide universal expressions for the first two
descendants in the identity family. We apply our technique to critical systems
belonging to different universality classes with non-trivial boundary
conditions that preserve conformal invariance, and find excellent agreement
with numerical results obtained for finite spin chains. We also demonstrate
that entanglement entropies are a powerful tool to resolve degeneracy of higher
excited states in critical lattice models.
