A septum for use in sealably covering a fluid cavity of an implantable medical device, such as an access port, is disclosed. The septum is resilient and includes a reinforcement structure that bolsters septum placement over the fluid cavity so as to inhibit unintended separation of the septum from the medical device when the fluid cavity is under pressure, such as during power injection of fluid into the fluid cavity. In one embodiment the septum comprises a resilient septum body that includes a flange disposed about a perimeter thereof. A reinforcement component is disposed in the flange for reinforcing engagement of the flange with a corresponding groove defined about an opening to the fluid cavity of the medical device so as to inhibit unintended detachment of the septum from the medical device. The reinforcement component in one embodiment includes an annular cord disposed in the flange.