Provided are a computer program product, system, and method for supporting non-delivery notification between a switch and device in a network. A login with a switch is initiated including a test service parameter requesting a non-delivery notification service to cause the switch to return a non-delivery notification in response to a test path request indicating a destination node that is unavailable. Indication is made that the test service is available for the login in response to receiving a reply from the switch that the switch accepts the login with the non-delivery notification service. The test path request is sent to the switch to determine whether the destination node is available in response to determining that the non-delivery notification service is available for the switch login. The non-delivery notification is received from the switch in response to the switch determining that the destination node to which the test path request is directed is unavailable.