Eigenvalue complementarity problems still have interesting theoretical properties that are not fully understood so far. Here, we are interested in local Lipschitzian error bounds. We first introduce the new class of ostensibly affine complementarity problems and derive conditions that characterize the existence of such an error bound for this class. These results are applied to eigenvalue complementarity problems. In particular, this allows us to prove the existence of a local Lipschitzian error bound for the symmetric linear eigenvalue complementarity problem.