A stent and associated method maintains a lacrimal duct in an open, unobstructed state following DCR. The self-expanding, bioresorbable tubular structure has a diameter in the range of 5-8 mm and a length in the range of 4-8 mm following self-expansion. A mesh structure includes struts interconnected through shape-memory hinge regions that open to facilitate expansion. The structure may assume an hour-glass form having a necked-down waist region and flared opposing end regions following expansion to assist in maintaining the stent in position. The stent is compressed to a diameter in the range of 1-3 mm, loaded into an inserter tool, and positioned into a lacrimal duct having an inner wall. The stent is inserted into the lacrimal duct, whereby the stent self-expands into a structure that conformally applies outward pressure to the inner wall of the lacrimal duct to hold open the duct, and the inserter tool is removed.