This was an interesting approach Tadvise took in checking tweets before they are sent for relevancy. They look at what you are about to send to your followers, including hashtags and help decide if your followers will retweet or even care about it. They also recommend some accounts that may retweet it. Where they get this list from was not clear and I wonder if they are sponsored in some way.
You must follow Tadvise before using the service. They have a good explanation page of why due to rate limits with the Twitter API and crawling. If you chose not to follow Tadvise and the site still works for you then someone you follow already follows them as they do seeding across followers on public accounts.
Also note that I never mention that authenticating or allowing access is needed to your Twitter account! This is great but also limits access to public Twitter accounts only. I am running tests now so this post will be updated soon.