The present disclosure describes an implantable branched vessel prosthesis, such as a prosthetic valve, having both a radially expandable annular portion and a laterally extendable branch portion. Methods of delivering the branched vessel prosthesis to a branched body vessel are also provided, as well as delivery systems comprising the branched vessel prosthesis. The branched vessel prostheses are useful, for example, as implantable prosthetic venous valves for treating venous valve insufficiency. The delivery system is configured to deploy independently both the annular portion within a primary vessel and the branch portion within a branch vessel with only one delivery system.