I routinely use Rapportive to guess email addresses and easily get to LinkedIn profiles.
Just put an email address in the To field and Rapportive will (90% or more of the time) show the person's LinkedIn profile if you've got it right. You can also hover your cursor over email addresses to change the Rapportive display to that person's information - really handy when you're copied on a group email and not sure who the rest of the recipients are.
Clicking on the LinkedIn logo to get to the person's profile page.
The only drawback I've seen in many years of using it is that lately I can't send a connection request directly from the Rapportive info in Gmail. I have to visit their actual LinkedIn profile page and click on connect the regular way. Not a big deal; just an error I've been getting consistently as of late.
Install it. Super easy to use and you start seeing the benefits immediately. Haven't found it to be a bloated extension or slowing anything else down in any way.
I've used Rapportive in a sales context, mostly for new business, but it's been really helpful in working with people I already know. It's a nice reminder to look someone up online to find mutual interests.