To date, I've used Credly to issue, receive and manage badges. Turns out it's simple to link Credly badges to LinkedIn, as well as embed Credly badges on any website with the supplied iFrame code.
Below is an embed of the Credly badges I have received for work toward an Open and Networked PhD. These same badges are now on my LinkedIn profile (in the form of a graphic link) in the Education section. Credly does support a more direct way of Add to Profile on LinkedIn, but only when the badges are issued from a verified Credly account.