I have same thing in my workilist. I need to change Servicedesk from http to https without totally reinstalling the software.

I have not started testing it but would like any info about it and I will post a solution if I come up with any

As far as I'm aware https can only be setup during initial setup of servicedesk so it would need a reinstall, but be aware you will take a 20% hit on performance if you use https because it needs to encypt/decrypt all transactions within the workflow, and this was told to me by a instructor who been doing helpdesk/servicedesk implementations for years.

If I remember correctly, during setup it was possible to enable HTTPS with Notification server. But we are talking here servicedesk portal? Usage of https is in Servicedesk settings during setup. It should be possible to change it later also.

I will try it and tell if it is possible. If someone has done this post install change please let me know so we will not make same mistakes =)

To use SSL or Https you must install with Https at the beginning of the install. 

Certain webparts will not function correctly if you install http and turn on https, in particular the report webpart is the one I have seen not function. This will also occur if you install http and put the server behind a load balancer that is running https. I believe that there is some setting done during the install to the webpart that must be set to http or https at the install. Same problem with the webpart will occur if the certificate expires.

Was on with support for full day before deciding a reinstall was required.