With the Syrian crisis still ongoing, 91% of Syrian refugee families in Lebanon do not have adequate access to safe and sufficient food. There has been a drive for technological innovation in humanitarian food assistance. To further inform such innovation, we used an Experience-Centred Design approach to gain a holistic understanding of the experiences of refugee food insecurity and how refugees envision technologies can support them. Design engagements with 13 women in an informal refugee settlement in Lebanon were conducted. The findings presented in this paper highlight that coping with food insecurity consists of experiences of adaptation, navigation, negotiation and sharing. We found that a multitude of technologies may be designed to enhance the aforementioned experiences and enable refugees to better cope with food insecurity. Through the lens of our findings, we discuss how technologies may support information sharing, the furthering of new practices and sharing of resources to support refugee food security.