Hi Andrew;
This is mostly all IIS work. You will need both Server and Client certificates obtainable from a certificate authority. Then the IIS machine needs to have its server certificate installed into the "Certificate Store" on that machine.
For the PS Web app, you should then change the provided HTTP web page source then to redirect the App start-up to an HTTPS invocation. At that point, the Client Certificate will be installed into the Browser machine's Certificate Store. Once the two certificates match, an HTTPS session will now commence.
Here is an example of what I use to do an HTTP => HTTPS "redirect" from within an HTML webpage ...
<!-- beginning of HttpRedirect.htm file -->
<script type="text/javascript">
function redirectToHttps()
{
var httpURL = window.location.hostname + window.location.pathname;
var httpsURL = "https://" + httpURL ;
window.location = httpsURL ;
}
redirectToHttps();
</script>
<!-- end of HttpRedirect.htm file -->
HTH
Regards ... Chris