Swap Commerce require an order reference to be sent which already exists in their system. Depending on the channels you use, the required order reference may appear as the "Shipment ID", "Order ID", or "Alternative 3rd Reference".
In your Swap Commerce configuration, you can choose which of your Shiptheory order references you would like to send to Swap:
If you encounter any issues, please feel free to contact our support team. You can call us on 0117 403 4313 (UK) / +1 (629) 666-6726 (US) or reach us online here.