The existence of quantum computers and Shor’s algorithm poses an imminent threat to classical public-key cryptosystems. These cryptosystems are currently used for the exchange of keys between servers and clients over the Internet. The Internet of Things (IoT) is the next step in the evolution of the Internet, and it involves the connection of millions of low-powered and resource-constrained devices to the network. Because quantum computers are becoming more capable, the creation of a new cryptographic standard that cannot be compromised by them is indispensable. There are several current proposals of quantum-resistant or post-quantum algorithms that are being considered for future standards. Given that the IoT is increasing in popularity, and given its resource-constrained nature, it is worth adapting those new standards to IoT devices. In this work, we study some post-quantum cryptosystems that could be suitable for IoT devices, adapting them to work with current cryptography and communication software, and conduct a performance measurement on them, obtaining guidelines for selecting the best for different applications in resource-constrained hardware. Our results show that many of these algorithms can be efficiently executed in current IoT hardware, providing adequate protection from the attacks that quantum computers will eventually be capable of.