We present the design of the Memory Machine (MeMa), a technology probe that can store, contextualise, and document media to represent memories. We accumulate vast physical and digital possessions throughout our lives, making it difficult to distinguish value in amassed images, albums, videos, mementos, and music. One option we wanted to explore via MeMa was to frame personal memories as a gift, in turn providing a way to revisit, share, and collate personal archives. We deployed MeMa into participants' homes and tasked them to create a digital gift involving an autobiographical memory. Through qualitative methods we uncovered the experience of twelve gift-givers. We found that the framing as a gift brought meaning to a collection of media, promoting reflection and emotional reminiscence in participants. Our contributions include design implications involving the relationship between emotions, technology, and gifting. CCS Concepts: • Human-centered computing → HCI theory, concepts and models.