Compared to traditional hardware development methodologies, High-Level Synthesis (HLS) offers a faster time-to-market and lower design cost at the expense of implementation efficiency. Although Software/Hardware Codesign has been used in many areas, its usability for benchmarking of candidates in cryptographic competitions has been largely unexplored. This paper provides a comparison of the HLS- andRTL-based design methodologies when applied to the hardware design of the Number Theoretic Transform (NTT) – a core arithmetic function of lattice-based Post-Quantum Cryptography (PQC). As a next step, we apply Software/Hardware Codesign approach to the implementation of three PQC schemes based on NTT. Then, we integrate our HLS implementation into the Xilinx SDSoC environment. We demonstrate that an overhead of SDSoC compared to traditional Bare Metal approach is acceptable. This paper also shows that an HLS implementation obtained by modeling a block diagram is typically much better than an implementation obtained by using design space exploration. We conclude that the HLS/SDSoC and RTL/Bare Metal approaches generate comparable results.