An everter device to facilitate preparation of ends of arterial segments for end-to-end microvascular anastomosis. The device includes structure that provides sufficient support to prevent unwanted buckling of arterial tissue. The everter device offsets the tendency of the arterial tissue wall to recover its natural shape and fall off securement posts or pins of a coupler ring. The structure may be in the form of an intraluminal catheter balloon. Alternately, the structure may be in the form of a plunger. Alternately, the structure may be in the form of a radially expanding member provided on a shaft. The device further has a contoured surface on an everter end to evert a free end of arterial tissue over a coupler ring, and to cause the posts or pins of the coupler ring to pierce through the everted arterial tissue. The everter end is provided with one or more openings therein, such as a circumferential slot, to receive the posts or pins of the coupler ring.