A port closure system with hydraulic hammer resistance, said system comprising: a port to establish communication between an interior volume that can receive a fluent substance and an exterior environment, the port having a laterally inwardly facing engaging surface; and a valve including a peripheral attachment portion and a flexible, resilient head extending across the port, the head having: an interior side facing the interior volume; an exterior side facing the exterior environment; at least one self-sealing slit through the head; head further comprising: confronting, openable portions along the slit to define a normally closed orifice in an unconstrained condition wherein the openable portions can move in a first direction toward the interior volume to an open orifice configuration and in a second direction toward the exterior environment to an open orifice configuration; and a laterally outwardly facing peripheral surface being frusto-conical with a maximum diameter adjacent the interior side and a minimum diameter adjacent the peripheral attachment portion of the valve, characterized in that the laterally outwardly facing peripheral surface is compressed laterally inwardly by engagement with the engaging surface to thereby impose a closing force on said self-sealing slit to increase the resistance of the normally closed orifice to opening in at least the second direction when the valve head is subjected to a pressure differential acting across the valve head. a port to establish communication between an interior volume that can receive a fluent substance and an exterior environment, the port having a laterally inwardly facing engaging surface; and a valve including a peripheral attachment portion and a flexible, resilient head extending across the port, the head having: an interior side facing the interior volume; an exterior side facing the exterior environment; at least one self-sealing slit through the head; head further comprising: confronting, openable portions along the slit to define a normally closed orifice in an unconstrained condition wherein the openable portions can move in a first direction toward the interior volume to an open orifice configuration and in a second direction toward the exterior environment to an open orifice configuration; and a laterally outwardly facing peripheral surface being frusto-conical with a maximum diameter adjacent the interior side and a minimum diameter adjacent the peripheral attachment portion of the valve, characterized in that the laterally outwardly facing peripheral surface is compressed laterally inwardly by engagement with the engaging surface to thereby impose a closing force on said self-sealing slit to increase the resistance of the normally closed orifice to opening in at least the second direction when the valve head is subjected to a pressure differential acting across the valve head. an interior side facing the interior volume; an exterior side facing the exterior environment; at least one self-sealing slit through the head; head further comprising: confronting, openable portions along the slit to define a normally closed orifice in an unconstrained condition wherein the openable portions can move in a first direction toward the interior volume to an open orifice configuration and in a second direction toward the exterior environment to an open orifice configuration; and a laterally outwardly facing peripheral surface being frusto-conical with a maximum diameter adjacent the interior side and a minimum diameter adjacent the peripheral attachment portion of the valve, characterized in that the laterally outwardly facing peripheral surface is compressed laterally inwardly by engagement with the engaging surface to thereby impose a closing force on said self-sealing slit to increase the resistance of the normally closed orifice to opening in at least the second direction when the valve head is subjected to a pressure differential acting across the valve head. confronting, openable portions along the slit to define a normally closed orifice in an unconstrained condition wherein the openable portions can move in a first direction toward the interior volume to an open orifice configuration and in a second direction toward the exterior environment to an open orifice configuration; and a laterally outwardly facing peripheral surface being frusto-conical with a maximum diameter adjacent the interior side and a minimum diameter adjacent the peripheral attachment portion of the valve, characterized in that the laterally outwardly facing peripheral surface is compressed laterally inwardly by engagement with the engaging surface to thereby impose a closing force on said self-sealing slit to increase the resistance of the normally closed orifice to opening in at least the second direction when the valve head is subjected to a pressure differential acting across the valve head.