Visiting Portofino is a sensual experience, and this being the case you should bring some of those sensual items back with you. There are a couple of small shops in the harbor area offering regional foods and wines for reasonable prices, and so providing a perfect way to extend your time there even after you've left.
If you're more into high fashion, there are several posh boutiques from some of the world's most famous designers, not surprisingly with some Italian luminaries on prominent display. If shopping is on your agenda you'll happily be able to peruse the latest designs from Armani, Gucci, Pucci, Ferragamo and Zegna. If you aren't looking for runway attire, there are also several boutiques with unique items, including one with lovely Murano glass jewelry.
Of course there are a few tourist shops and kiosks as well, with the usual assortment of beads, magnets and t-shirts for your browsing pleasure.