The syntax that you have posted is incorrect, though from your original post I suspect that you may already know this. Correct would be I've tested this, including when there is a zenid in the URL and it works fine. If with correct syntax it's not working for you, and/or you are seeing zenid in the URL a lot then I suspect you have a rather different problem.
zenid should only appear on the first click on a site, or when you click on a secure page (which your EZ-Pages would not normally be). If you are experiencing something different, I would recommend taking a look at
this thread.