Example methods and apparatus to diagnose outbound voice over Internet protocol (VoIP) services are disclosed. An example method comprises monitoring activity in a first VoIP network to determine a first value representative of a peak number of communication sessions concurrently active between a second VoIP network and a public switched telephone network via the first VoIP network, and comparing the first value to a threshold to determine whether to automatically close a trouble ticket submitted against the first VoIP network.