Wine glasses have wide rims, which can fit a cupcake perfectly. All you need to do is turn the wine glass upside-down and place it directly over the cupcake.
Just make sure the glass is tall and wide enough to house the cupcake and has a perfectly flat rim that will sit flush with the counter or plate on which your cupcake sits.
Cupcakes with no frosting or filling will stay fresh for about a week as long as they're properly stored, but if the cupcake is frosted or filled, it will last three to four days.