My 0,05€ on this.
Runbox indeeds supports CalDAV and CardDAV.
However, it lacks support for something as basic as sending e-mail invitations: worse than that, it actually worked and now it is not working.
(This was posted in https://community.runbox.com/t/announcement-runbox-7-calendar-beta/815/52?u=dourado)
So, basically, one can receive calendar invitations, but it cannot send since a few weeks ago. As for the web interface, it was never possible to send invitations that way (only via apps like Google Calendar or Thunderbird).