As we go about our everyday routines we encounter and interact with numerous physical (e.g. furniture or clothes) and digital objects (e.g. photos or e-mails). Some of these objects may be particular cherished, for example because of memories attached to them. As several studies into cherished objects have shown, we have more difficulties identifying cherished digital objects than physical ones. However, cherishing a small collection of digital objects can be beneficial; e.g. it can encourage active selection of digital objects to keep and discard. This paper presents a study that aimed to increase understanding of cherished physical and digital objects, and beyond that, of how we perceive physical and digital objects, and their advantages and disadvantages. We identified design opportunities for novel products and systems that support the creation of more cherishable digital objects by extrapolating the advantages of the physical to the digital, exploiting the reasons for cherishing digital objects, and aiming for meaningful integrations of physical and digital.