X.509 is the de facto digital certificate standard used in building the Public Key Infrastructure (PKI) on the Internet. However, traditional X.509 certificates are too heavy for battery powered or energy harvesting Internet of Things (IoT) devices where it is crucial that energy consumption and memory footprints are as minimal as possible. In this paper we propose, implement, and evaluate a lightweight digital certificate for resource-constrained IoT devices. We develop an X.509 profile for IoT including only the fields necessary for IoT devices, without compromising the certificate security. Furthermore, we also propose compression of the X.509 profiled fields using the contemporary CBOR encoding scheme. Most importantly, our solutions are compatible with the existing X.509 standard, meaning that our profiled and compressed X.509 certificates for IoT can be enrolled, verified and revoked without requiring modification in the existing X.509 standard and PKI implementations. We implement our solution in the Contiki OS and perform evaluation of our profiled and compressed certificates on a state-of-the-art IoT hardware.