I’ve seen a growing group of others who are using and displaying Webmentions for site-to-site conversations. If you use WordPress, there’s the Webmention plugin for the notifications part and the Semantic Linkbacks plugin for the display part. (One day the two will merge, we hope.)
Plugins and modules exist for a number of other systems if they’re not already built in.
I’m using all these on my site to have site-to-site conversations with others. I’m also using Brid.gy to bridge the gap between WordPress and Twitter (and others). If you prefer, you could read all this on my site.
Happy to help others set this up for themselves, should they need help. #DoOO