Determining the optimal arrangement of superconducting layers to withstand large-amplitude ac magnetic fields is important for certain applications such as superconducting radio-frequency cavities. In this paper, we evaluate the shielding potential of the superconducting-film-insulating-film-superconductor (SIS′) structure, a configuration that could provide benefits in screening large ac magnetic fields. After establishing that, for high-frequency magnetic fields, flux penetration must be avoided, the superheating field of the structure is calculated in the London limit both numerically and, for thin films, analytically. For intermediate film thicknesses and realistic material parameters, we also solve numerically the Ginzburg-Landau equations. It is shown that a small enhancement of the superheating field is possible, on the order of a few percent, for the SIS′ structure relative to a bulk superconductor of the film material, if the materials and thicknesses are chosen appropriately. © 2015 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the «http://creativecommons.org/licenses/by/3.0/» Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.