Ensuring communication security in real-time automotive networks is of paramount importance given the sensitivity of the exchanged information and highly safety critical nature of its operation. The first step towards ensuring security is to securely authenticate all the computational nodes through use of authentication protocols based on public-key cryptography. But, traditional public-key cryptographic primitives we use today are believed to be breakable by large scale quantum computers of the future. Thus, NIST is currently running a global global level standardization process for quantum-resistant public-key cryptography, better known as post-quantum cryptography. In this work, we perform a first of its kind practical implementation of a secure authentication protocol for automotive systems with post-quantum cryptographic algorithms and perform a detailed comparative evaluation of the speed and communication bandwidth performance against their pre-quantum counterparts.