Disclosed herein are proximally-flaring stents and balloon catheter systemsand methods for using the same to restore patency to a side branch and itsostium at a vessel bifurcation, where the side branch can only be approachedfrom the direction of the main artery. The system and methods include aproximally-flaring stent (10) and one or more balloon catheters (250, 400)with inflatable balloons that are able to push a flanged proximal portion (40)of the proximally-flaring stent entirely against the artery walls of the mainartery of the side branch so that blood flow is not occluded.