Like many health devices, smart pill boxes designed to enhance medication adherence often incorporate electronic components and smart sensors. However, the production and disposal of these rising numbers of electronics contribute significantly to the global e-waste crisis, exacerbating the negative climate impact of the healthcare industry. To minimize the impact of such electronic health devices, redesign based on circular economy principles is crucial. However, currently no clear circular design methodology exists to apply those principles in the healthcare domain. This paper discusses a case study in which we propose conceptual redesigns that aim to mitigate the environmental impact of smart pill boxes and help align them with circular economy principles. We employ a research-through-design approach in which we attempt to apply the well-known '10R strategies' (i.e. refuse, rethink, reduce, reuse, repair, refurbish, remanufacture, repurpose, recycle, and recover) as a design method. While doing this, we assessed their applicability in a design process and added value in making the device circular through reflective journalling, and their estimated effectiveness on minimizing environmental impacts by comparing fast-track LCAs for each design decision. In this way, we were able to provide insights into the intricacies of designing a more sustainable and circular device in this manner, and subsequently formulate recommendations for designing similar devices in the future.