Disclosed is an implantable medical port and methods of using the implantable medical port to deliver and/or to withdraw a desired agent, such as medicines, treatments, or any other fluid into and/or from a body of a subject. The implantable medical port includes two or more needle-penetrable septum portions to provide an increased needle penetration area. Also provided is an implantable medical port having a fluid cavity the contains a substantially needle-impenetrable member that prevents a needle from inadvertently puncturing or otherwise damaging a septum portion other than the septum portion that was initially punctured to gain access to the fluid cavity.