Techniques are described for providing managed virtual computer networks whose configured logical network topology may have one or more virtual networking devices, such as by a network-accessible configurable network service, with corresponding networking functionality provided for communications between multiple computing nodes of a virtual computer network by emulating functionality that would be provided by the networking devices if they were physically present. The networking functionality provided for a managed computer network may include supporting a connection between that managed computer network and one or more other managed computer networks, such as via a provided virtual peering router to which each of the managed computer networks may connect, with the functionality of the virtual peering router being emulated by modules of the configurable network service without physically providing the virtual peering router, including to manage routing communications between the inter-connected managed computer networks in accordance with client-specified configuration information.