It turns out that you need to understand two things to make this work.
In the Template Editor when you press Insert/Update there is no option for the contactid.
#1 Generating a contact id
{!contact:contactid;}
Now Save the Template and this text will turn into a working merge field that returns the contact id of the contact the email is being sent to.
{!Contact:Contact;}
#2 Be careful about links in the Email Template Editor
The following line will be merged properly and the contact's email browser will typically display a link.
https://www.myportal.com/OrderService.aspx?id={!Contact:Contact;}&type=0
This line may surprise you since the email will look fine but the link won't work.
https://www.myportal.com/OrderService.aspx?id={!Contact:Contact;}&type=0
What you get is the following:
Notice that the text of the link is merged, but the href value is not.
What if you want a nicely formatted link?
Please click here to find out more!At this point I "believe" your only course of action is to manually modify the XML in the email template body in SQL. I haven't tried that yet, but will post additional information if I do.