A ring for use in preparing a first organ for anastomosis with a second organ, wherein the first organ has an orifice, and the ring has a central ring portion sized to extend around the orifice and malleable tines that extend from the ring portion. The ring portion is configured to dilate and contract radially relative to the central axis. Malleable tines may extend out from the ring portion. The tubular shape of the ring provides rigidity parallel to the central axis thereof and flexibility in directions perpendicular to the central axis. In another class of embodiments, the central ring portion is a tubular member, which is preferably but not necessarily capable of dilating and contracting radially relative to the central axis. In some embodiments, the central ring portion includes rigid sections alternating with bowed sections, each of the bowed sections functioning as a spring capable of flexing to allow the rigid sections adjacent thereto to move radially inward and outward. In other embodiments, the central ring portion includes rigid sections, which can be made of metal, alternating with elastic sections, which can be made of elastomeric material such as silicone rubber or superelastic material or memory metal. Installation tools are also provided.