Methods and devices for forming an anastomosis between hollow bodies utilize magnetic force to couple anastomotic securing components and connect the lumens of the hollow bodies. End-to-side, side-to-side and end-to-end anastomoses can be created without using suture or any other type of mechanical fasteners, although such attachment means may be used in practicing some aspects of the invention. The securing components have the ability to produce a magnetic field and may include materials or assemblies. A component may also be used to form a port into the lumen of a vessel, the component being attached to the vessel by mechanical and/or magnetic means. Magnetic components may include means for concentrating the magnetic flux between respective components to increase the attraction force, thereby enhancing the security of the anastomosis. Also, rather than form a port communicating with a lumen of a vessel or other cavity, the components may have an occlusion surface and be used to close an opening in tissue, e.g., an atrial septal defect.