After doing several varied searches, here is the only answer I could find…it seems that if your customer is new to z that creating an account is the only way to get a shipping estimate. Or they could try calling customer support. (International orders have a different answer)
Calculating Your Shipping Costs
Given the many variables in generating a shipping quote, we recommend you use the tools available to you on our site to get the most accurate pricing. You need not make a purchase to do so.
You can generate a shipping price quote by adding the items you are considering for purchase to your shopping cart. If this is your first time using the Zazzle checkout, you may be asked to create a Zazzle account, and to add a shipping and billing address in order to proceed onto the page with the shipping estimates. Rest assured that you will not be charged unless you proceed all the way through to the completion of your order (and the Order Confirmation page).
Once you have entered the requested information needed to provide the estimate, the various available shipping options, and relative pricing will be displayed. This page will also reflect an overall price for the order, including product, tax (if applicable), commission, packing, transport, insurance, and other incidental costs.*
Please note that both product & shipping prices are subject to change. Quotes generated using the method noted above are only valid for the browser session during which they are generated. Prices displayed during previous sessions will not be honored.
*The cart does not reflect customs duties for internationally bound packages ordered through the Zazzle.com site. For more information on import taxes, please contact your local customs office.
