This paper discusses Digital Environmental Stewardship as an analytical framework that can help HCI scholarship to understand, design, and assess sociotechnical interventions concerned with sustainable waste management practices. Drawing on environmental studies, we outline key concepts of environmental stewardship - namely actors, capacity, and motivations - to unpack how different initiatives for handling waste are organised, both through grassroots and top-down interventions, and through varying sociotechnical configurations. We use these dimensions to analyse three different cases of waste management that illustrate how actions of care for the environment are ecologically organised, and what challenges might hinder them beyond -or besides- behavioural motivations. We conclude with a discussion on the orientation to action that the suggested framework provides, and its role in understanding, designing and assessing digital technologies in this domain. We argue that examining how stewardship actions fold into each other helps design sociotechnical interventions for managing waste from within a relational perspective.