Apiary secures all connections if those are requested with
https:// protocol. Your API documentation is hosted on a fourth level domain (e.g.
https://docs.<yourdomain>.apiary.io). Unfortunately, no certification authority is able to issue a certificate supporting wildcard for more than one domain level. As a result, the browser may display a warning indicating that the certificate is not trusted, although the connection is properly secure.
If you need your API Documentation trustfully secured, you can use Apiary Embeddable Documentation hosted on your own secured domain. Embeddable Documentation is part of Apiary Pro, which you can try it now free of charge.