Preventing Online Sales of E-Cigarettes to Children Act This bill revises requirements regarding the sale and delivery of electronic nicotine delivery systems (e.g., e-cigarettes, e-hookah, e-cigars, and vape pens). Specifically, the bill subjects the sale and delivery of these systems to certain requirements, including tax, licensing, and labeling requirements; prohibits the sale and delivery of these systems to anyone under the legal age to purchase tobacco products; and requires the U.S. Postal Service to implement regulations to prohibit the mailing of these systems. The bill does not apply to products approved by the Food and Drug Administration for tobacco cessation or any other therapeutic purposes.