Widely used asymmetric primitives such as RSA or Elliptic Curve Diffie Hellman (ECDH), which enable authentication and key exchange, could be broken by Quantum Computers (QCs) in the coming years. Quantum-safe alternatives are urgently needed. However, a thorough investigation of these schemes is crucial to achieve sufficient levels of security, performance, and integrability in different application contexts. The integration into Transport Layer Security (TLS) plays an important role, as this security protocol is used in about 90% of today’s Internet connections and relies heavily on asymmetric cryptography. In this work, we evaluate different Post Quantum Cryptography (PQC) key establishment schemes in TLS 1.3 by extending the framework of Paquin et al.. We analyze the TLS handshake performance under variation of network parameters such as packet loss. This allows us to investigate the suitability of PQC KEMs in specific application contexts. We observe that Kyber and other structured lattice-based algorithms achieve very good overall performance and partially beat classical schemes. Other approaches such as FrodoKEM, HQC and BIKE show individual disadvantages. For these algorithms, there is a clear performance decrease when increasing the security level or using a hybrid implementation, e.g., a combination with ECDH. This is especially true for FrodoKEM, which, however, meets high security requirements in general. It becomes clear that performance is strongly influenced by the underlying network processes, which must be taken into account when selecting PQC algorithms.