SSL between web applications on the same computer

I have two java web applications installed on the same machine exchanging HTTP, security is a big concern as application A checks the license of application B.

I believe there is no point in enabling HTTPS as we probably cannot hide the application. Private key, rendering HTTPS useless.

Is there a way to enable HTTPS in this scenario so that it makes sense to use it? I'm not sure if this is relevant, but Appendix A is quite small, so hiding the private key is probably even more difficult.