Noncontiguous Shipping Relief Act of 2023 This bill establishes a limited exception to coastwise laws to allow foreign-flag freight vessels to transport merchandise domestically to or from a port in the noncontiguous United States. The bill also addresses various issues related to foreign-flag freight vessels engaged in coastwise trade (i.e., domestic waterborne trade between U.S. ports). Under the coastwise laws, commonly known as the Jones Act, a freight vessel may not transport merchandise between U.S. ports unless it is U.S.-built, at least 75% owned by U.S. citizens, and mostly crewed by U.S. citizens. The bill authorizes qualifying foreign-flag vessels to transport merchandise between (1) a port in the contiguous United States and a port in the noncontiguous United States (i.e., Alaska, Hawaii, Puerto Rico, or a U.S. territory or possession); or (2) two ports in the noncontiguous United States. Under the bill, all foreign-flag freight vessels operating in U.S. coastwise trade must comply with the (1) minimum international labor standards applicable to U.S. seafarers, and (2) same environmental standards that apply to U.S. vessels. The bill authorizes such operators to participate in the Longshore and Harbor Workers’ Compensation program on behalf of masters and crew members they employ. The bill also requires foreign-flag vessel owners and operators engaging in coastwise trade to identify an agent for service of process, abide by U.S. tax and other laws, and maintain specified documentation on board. Additionally, lawsuits against such vessels alleging personal injury or death must be brought in U.S. district court.