Disclosed are devices and methods for delivering several sutures accurately and simultaneously around the perimeter of an annular prosthetic device (prosthetic heart valve, annuloplasty ring, etc.) to secure the prosthetic device within a native heart valve region. Devices can comprise a proximal handle portion including an actuator and a distal suturing portion including several curved and straight needles arrayed around the shaft axis. The straight needles and the curved needles are configured to simultaneously guide a plurality of sutures through the native tissue and through the annular prosthetic device. The actuator can cause the straight needles to move axially relative to the curved needles and can also cause the curved needles to rotate, such that the motions are coordinated to simultaneously place all the sutures.