In this tip Mike Snow explains how to send an email via Silverlight.
However, as with most things, you can leverage a Silverlight-enabled WCF server to do the dirty work for you. In this steps below I will be showing you the code needed to send the email through the SmtpClient object as well as some minor configurations you need to do to your server to get it working.
You may also want to take a look at Mike's previous tip on how to switch your service reference back to localhost.