Exemplary embodiments comprise AV fistulas and other anastomotic devices for creating new or reinforcing existing side-branch vessels, and/or bridging neighboring vessels together. An exemplary embodiment may comprise a sidewall port, such as a flanged sidewall port, and/or flow frame design, such as a partially bare, flexible stent or a whisk, for purposes of creating a transmural flow. Another exemplary embodiment may comprise a compliant vessel support to aid in the transition from device to vessel and/or vessel to device, and to promote vessel dilation.