Resilient Highways Act This bill addresses projects to increase the resiliency of federal-aid highways and bridges on and off the National Highway System. Specifically, the bill allows states to use up to 15% of funds apportioned under the national highway performance program for projects to mitigate the risk of recurring damage or the cost of future repairs from extreme weather, flooding, and other natural disasters on infrastructure that is part of the National Highway System; provides for a maximum federal cost-share of up to 100% for these projects; and authorizes emergency relief funds to be used to pay for these projects, including removing debris from rivers, creeks, streams, and ditches, raising roadway grades, deepening channels to prevent flooding, improving drainage, and stabilizing slopes.