Content-Centric Networks (CCNs) are fundamental evolutionary technologies that promise to form the cornerstone of the future Internet. The information flow in these networks is based on named data requesting, in-network caching, and forwarding -- which are unique and can be independent of IP routing. As a result, common IP-based network tools such as ping and traceroute can neither trace a forwarding path in CCNs nor feasibly evaluate CCN performance. We propose "contrace," a network tool for CCNs (particularly, CCNx implementation running on top of IP) that can be used to investigate 1) the Round-Trip Time (RTT) between content forwarder and consumer, 2) the states of in-network cache per name prefix, and 3) the forwarding path information per name prefix. We report a series of experiments conducted using contrace on a CCN topology created on a local testbed and the GEANT network topology emulated by the Mini-CCNx emulator. The results confirm that contrace is not only a useful tool for monitoring and operating a network, but also a helpful analysis tool for enhancing the design of CCNs. Further, contrace can report the number of received interests per cache or per chunk on the forwarding routers. This enables us to estimate the content popularity and design more effective cache control mechanisms in experimental networks.