Many authentication methods have been proposed to authenticate GNSS and SBAS civil signals in response to signal interference threats. These proposed methods utilize contemporary cryptographic standards. However, quantum computing poses a threat to currently existing authentication schemes that may render them insecure. Thus, it is vital to implement authentication methods that are quantum resistant to protect GNSS and SBAS signals well into the future. This paper briefly discusses the impact of quantum computing on contemporary cryptographic standards. A review of the post-quantum digital signature authentication schemes from the NIST post-quantum cryptography standardization competition is presented. Schemes that are applicable to GNSS and SBAS authentication are then identified. Next, a brief introduction to multivariate cryptography is presented. The paper concludes with a discussion on how the post-quantum schemes can used to authenticate GNSS and SBAS data.