Apparatus and methods for creating anastomoses are provided. An incision tool for creating an incision having a controlled length in a side wall of a patient's body tissue conduit is provided. A delivery device for inserting a hollow annular connector into an incision in a side wall of a patient's body tissue conduit is provided. The delivery device may include first and second anvil structures around which the connector may be disposed. By moving the first anvil structure away from the second anvil structure, the connector may expand to a desired configuration (e.g., non-round) within the aperture. In one example, the connector may be inserted into the aperture to hold the aperture open prior to attachment of a graft conduit to the aperture, thereby allowing a physician to inspect the aperture and the surrounding tissue.