I wouldn't recommend approaching them via email as it will probably be viewed as spam since it's unsolicited.

I'd first make an effort to find out who's in charge of making decisions about such things. Then I'd contact that person by phone and ask them if they've considered updating their web site and—if they seem open to the idea—ask if you can set up a meeting to show them your web design portfolio. If they're not in the same city, you could offer to send them a brochure and/or email them a link to your online portfolio.

Be sure that you're very diplomatic when discussing the existing the site as you never know when it might have been built by the person you're speaking to (or a close coworker, friend, etc.) You also need to have strong selling points: How did you find out about their site? In what ways will a redesign benefit them aside from making it "prettier"? Will it improve their search engine rankings? If so, how? Can you build them a CMS that will save them money in the long run? Why should they choose you over another designer? Etc.

Digi