As disinformation becomes increasingly sophisticated and difficult to verify – using advanced and widespread technologies such as generative AI and other forms of digital manipulation of content – there is a need to equip fact-checkers, journalists and media researchers with efficient verification tools, and to develop design frameworks for these tools. The EU-funded vera.ai project is taking on this task by developing a series of AI-based services as part of verification toolkits. These services aim to not only support their users in analyzing and determining the veracity of a piece of content, but to also do it in a way that fits into user workflows rather than modify them, as well as help users assess whether they can trust and rely on the analysis results. One of the concepts that the design of these tools is based on, is trustworthiness by design. In this paper, we describe our approach to centering workflow and trustworthiness, in designing AI-based tools against disinformation: highlighting how trustworthiness is not just about model reliability but also about putting users in control of the fact-checking process and about providing them with the opportunities to assess this reliability, by design. We thereby provide a case study in designing trustworthy AI-based verification tools for fact-checking that fit into user workflow, as well as a design framework for this type of tools, as a ground for better design and future research in this area.