A port closure system (20) including a retention structure (22), and a valve (24). The retention structure (22) includes a port (28) for establishing communication between an exterior environment (30) and interior volume (32) that can receive a fluent substance. The valve (24) includes a flexible, resilient, self-closing, slit-type valve head (36) with an orifice that is normally closed in an unconstrained condition. The port (28) has a laterally inwardly facing engaging surface (34) and the valve has a laterally outwardly facing peripheral surface (54) that is compressed laterally inwardly by engagement with the surface (34) to increase the resistance of the normally closed orifice to opening when the head (36) is subjected to a pressure differential. The system (20) further includes an annular flange (62) located to extend over at least a portion of an exterior side (38) of the valve head (36) to limit movement of the valve head (36) towards the exterior environment (30).