No Child Support, No Passport Act - Authorizes the Secretary of State to refuse, revoke, restrict, or limit a passport if the applicant or passport holder: (1) is a noncustodial parent who is the subject of an outstanding arrest warrant for nonpayment of child support, where the amount in controversy is not less than $5,000; and (2) is a custodial parent who is likely to remove the child from the United States for the purpose of preventing contact permitted between the child and the noncustodial parent.