Capsules in National Ignition Facility targets are conventionally supported by thin polymer films. Recent experiments have shown that these films add significant perturbations to the implosion. Here, we evaluate stiffer polyimide composite films for use in a new target design that has been predicted to reduce these perturbations. The films are evaluated by their contact radius to the capsule for different deflections and the force they generate at those deflections to center the capsule. We find that a composite film with a single-sided coating of carbon produces the best results and show the performance of these films in target assemblies, highlighting the importance of the indentation depth.