Being inspired by Kaplan's proposal for simulating chiral fermions on a lattice, we examine the continuum analogue of his domain-wall construction for two-dimensional chiral Schwinger models. Adopting a slightly unusual dimensional regularization, we explicitly evaluate the one-loop effective action in the limit that the domain-wall mass goes to infinity. For anomaly-free cases, the effective action turns out to be gauge invariant in the two-dimensional sense.