Caps, containers embodying such caps, and methods of enhancing cap safety. Air flow passages through the cap enable one, who accidentally swallowed the cap, to breathe/pass air through the cap. Some air passages extend top to bottom. Openings in the outer side wall, and an air flow path across the cap, allow air to enter the cap on a first side, flow transversely through the cap, and exit an opposing side. The top-to-bottom air flow passages, and the air flow path across the cap, including the openings in the outer wall of the cap, collectively support air flow through the cap, thus through the person's airway, if/when the cap becomes accidentally lodged in a person's airway. The openings can be used to engage and extract an accidentally swallowed cap. Elements of an optional tamper evident ring remain attached to the cap after the cap is removed from the container.