Over- The-Air (OTA) update is an innovative paradigm that is rapidly spreading through the automotive industry. Software updates can be capillary distributed thanks to the many Vehicle-to-Everything (V2X) communication infrastructures that are part of a Smart City. Unfortunately, the majority of the existing OTA frameworks and schemes are not quantum resistant, meaning that when quantum computing will become reality, they will not be secure anymore. The U.S. National Institute of Standards and Technology (NIST) has announced a contest to determine the post-quantum standards for digital signatures schemes. In this paper, we evaluate the performance of the digital signature verification algorithms of two out of the three finalists for the NIST contest, namely FALCON and CRYSTALS-DILITHIUM. These algorithms are tested on automotive-oriented evaluation board, namely the Xilinx Zynq Ultrascale+ ZCU102. The results show that FALCON is a more promising algorithm compared to DILITHIUM both regarding signature verification execution time and signature size.