The best solution would be to set up an automation rule to catch those orders that make it through your product defaults, service mappings, and other automation rules so that you can then assign those orders their appropriate carrier and method. You can even use this to catch holes in your other automation rules so that you can then tweak your settings to automate as many of your processes as possible.
First, we'll need to create the filter to catch the orders that come in without shipping carrier and method.
Head to your Account Settings (the wrench icon in the upper right).
Next, select Automation and then Automation Rules from the sidebar on the left.
Now, click on the Create Rule button.
Name your rule, and click the radio button next to "Only apply these actions to orders that match specific criteria."
Select + Add Criteria. Here, you'll need to choose "Requested Service (Mapped)" from the first drop-down, and then choose "Is blank" from the second.
You'll now need to add what you want to happen when an order comes in without a shipping method by adding an action. Here are a few examples:
- Add an Order Tag to mark the order as "No Service"
- E-mail you that orders came in without a shipping service
- Just set a carrier and method
By clicking the Add an Action button, you'll be able to see the full list of actions that you could take. Go ahead and do that for this rule, and then Save your changes.
Now, any order that comes in without a shipping method will have your chosen action applied to it.