Context. Centaurs are icy objects in transition between the trans-Neptunian region and the inner solar system, orbiting the Sun in the giant planet region. Some centaurs display cometary activity, which cannot be sustained by the sublimation of water ice in this part of the solar system, and has been hypothesized to be due to the crystallization of amorphous water ice. Aims. In this work, we investigate centaurs discovered by the Outer Solar System Origins Survey (OSSOS) and search for cometary activity. Tentative detections would improve understanding of the origins of activity among these objects. Methods. We search for comae and structures by fitting and subtracting both point spread functions and trailed point-spread functions from the OSSOS images of each centaur. When available, Col-OSSOS images were used to search also for comae. Results. No cometary activity is detected in the OSSOS sample. We track the recent orbital evolution of each new centaur to confirm that none would actually be predicted to be active, and we provide size estimates for the objects. Conclusions. The addition of 20 OSSOS objects to the population of ~250 known centaurs is consistent with the currently understood scenario, in which drastic drops in perihelion distance induce changes in the thermal balance prone to trigger cometary activity in the giant planet region.