In a discussion, I found that copying a SharePoint Calendar event between calendars in SharePoint using a workflow would fail. For some reason, it didn't think the destination calendar had the same fields. Support for that will be coming in a future release of Nintex Workflow. But for now, we can take the long way.
Rather than using the Copy Item action, we use the Create Item action and set each of the fields. If you take a look at an Event content type, there aren't really that many fields. So a simply Create Item action, configured with lookups to the source event is really not that hard or time consuming.
Event Content Type
So when it comes to copying a calendar item, as long as you can find it someway (eg. via an ID or a title), you'll be able to create a new calendar item, in another list with the same information.
Creating a New Event
To create a new event, based on an existing event, we simply add a Create Item action to our workflow. If you know the ID of the items you want to copy, you simply use lookups for all the fields you're interested in.
As you can see, it's quite easy to do. There are a few more configuration steps, but it does work.
Let me know if you find other ways (eg. web service calls) to do the same things.