1. A non-transitory computer-readable storage medium having stored contents that cause one or more computing systems of a configurable network service to at least: provide, by the configurable network service, a first virtual computer network; connect the first virtual computer network to a second virtual computer network provided by the configurable network service via a virtual peering router provided by the configurable network service, wherein at least one computing system of the one or more computing systems hosts one or more virtual machines used as computing nodes of the first virtual computer network; update, based at least in part on the connecting, configuration of the at least one computing system for use in managing communications between the one or more virtual machines and other computing nodes of the second virtual computer network, the updating including storing mapping information on the at least one computing system about at least one of the other computing nodes of the second virtual computer network; and forward, using the updated configuration, one or more communications from the one or more virtual machines to the other computing nodes and emulate functionality of the virtual peering router as part of the forwarding.