I was able to find some information on Framework 4.5 and the integration of SSL certificates to a RESTful web API over at the ASP.net development center. Here are instructions on working with SSL in Web API:
http://www.asp.net/web-api/overview/security/working-with-ssl-in-web-api
In addition, I was able to locate some resources on configuring a port to work with SSL when creating a self-hosted Windows Communication Foundation (WCF) service. This information may also be useful to you.
https://msdn.microsoft.com/en-us/library/ms733791(v=vs.110).aspx
If you have any other qustions, please let us know. We're always happy to help.