The rise of the Internet has enabled new types of relationships and online domains where trust must be computed rather than earned. However, classic trust and reputation techniques designed to support computational trust among Internet entities do not meet the scalability requirements and the resource constraints typical of Internet of Things (IoT) devices. This paper provides a general framework for managing computational trust where Blockchain technology and reputation systems are used in conjunction. Our framework relies on a reward-penalty scheme to offer a customizable, secure, and scalable trust architecture for IoT devices and the services they access. We implemented and tested a smart contract-based proof-of-concept, carrying out an analysis of its cost and security to verify the practical viability of our solution.