A cap for a container (e.g., container fitment) includes a neck portion and a lip portion that extends laterally outward from the neck portion. A gasket is provided between the cap and a rim of a container fitment. The neck portion is conical or frustoconical in shape, and an interior surface of a container port or fitment may be correspondingly tapered, to guide the cap into concentric alignment with the gasket and rim during insertion of the neck portion of the cap into the fitment. Such alignment promotes positive sealing engagement between the cap, gasket, and fitment. In one embodiment, the cap defines an externally accessible recess that optionally includes a handle, such as at least one segmenting wall, for grasping by a user to facilitate manipulation of the cap. The cap may be affixed to a fitment of a flexible liner.