Ships are technologies of maritime mobility. But sometimes ships are immobile—they stop and remain stationary for short or prolonged times. A degree of stasis inside and outside ports is both usual and essential for facilitating the movement of ships in global markets. This paper makes two important points: first, echoing existing literature, frequent stationarity (or waiting) is a normal occurrence in the industry. Second, it is not just mobilities that are disrupted via moments of stasis; immobilities themselves have distinct patterns that too can be disrupted. This nuance is vital: there is a need to understand the disruptions to immobilities rather than understanding immobilities as disruptions to the general condition of mobility, both within—and beyond—the shipping example. We argue that understanding disruptions to immobilities is vital to grasping the dynamics of shipping, alongside other (im)mobilites (car, train, plane), their conditions, and the politics that shape our world on the move. Using a data-driven approach, embracing AIS methods for exploring ship stationarity around US waters during the COVID-19 pandemic, this paper upends the assumptions of ship (im)mobilities through the example of wait times, calling for scholars to give space and time to everyday immobilities and their disruptions too.