Could you find an inexpensive card/ID holder that the cards would fit into? You could then box/wrap that.
Or you could make a mini album using name badge holders (verify the giftcards will fit first) and maybe use images/embellishments that go with the giftcard (for example shoes for a DSW gc, tools for a Home Depot gc. etc.)
Or you could make a fantasy box and put the giftcards in the drawers. There should be a tutorial in the resources section of this site.
Or you could find/make the smallest box a gc would fit into and find/make additional boxes, each one slightly larger than the previous box, so you'd have a tower/pyramid of boxes (each with a giftcard).