Many high-demand digital services need to perform several cryptographic operations, such as key exchange or security credentialing, in a concise amount of time. In turn, the security of some of these cryptographic schemes is threatened by advances in quantum computing, as quantum computer could break their security in the near future. Post-quantum cryptography (PQC) is an emerging field that studies cryptographic algorithms that resist such attacks. The National Institute of Standards and Technology (NIST) has selected the CRYSTALS-Kyber Key Encapsulation Mechanism and the CRYSTALS-Dilithium Digital Signature algorithm as primary PQC standards. In this article, we present field-programmable gate array (FPGA)-based hardware accelerators for high-volume operations of both schemes. We apply high-level synthesis (HLS) for hardware optimization, leveraging a batch processing approach to maximize the memory throughput and applying custom HLS logic to specific algorithmic components. Using reconfigurable FPGAs, we show that our hardware accelerators achieve speedups between 3 \(\times\) and 9 \(\times\) over software baseline implementations, even over ones leveraging CPU vector architectures. Furthermore, the methods used in this study can also be extended to the new CRYSTALS-based NIST FIPS drafts, ML-KEM and ML-DSA, with similar acceleration results.