Configuration binding extension 'system.serviceModel/bindings/basicHttpsBinding' could not be found

BasicHttpsBinding is a new binding in .NET 4.5, therefore you cannot use it in a 4.0 application. Either you remove the protocolMapping or you use another binding such as basicHttpBinding or wsHttpBinding.

When you configure SSL in IIS, this should work as well.

If you have a similar scenario as mine where the Visual Studio-generated Web.config has the following configs:

  <system.web>
    <compilation debug="true" targetFramework="4.5" />
    <pages controlRenderingCompatibilityVersion="4.0" />
  </system.web>

... add <httpRuntime targetFramework="4.5" />

So that you now have

  <system.web>
    <compilation debug="true" targetFramework="4.5" />
    <pages controlRenderingCompatibilityVersion="4.0" />
    <httpRuntime targetFramework="4.5" /> 
  </system.web>

I also went on to remove <pages controlRenderingCompatibilityVersion="4.0" /> with no impact in my situation.