Consider a remote sensing system where multiple pairs of stochastic subsystems and corresponding non-collocated estimators share a common wireless network. In order to avoid packet collisions, the access to the network is mediated by a manager that chooses, based on the realizations of the states, which one (if any) of the states will be transmitted over the network. Each estimator is interested solely on the state of its corresponding subsystem. This paper studies the jointly optimal design of scheduling and estimation strategies for a cost functional consisting of a mean-squared error and a communication cost in a one-shot problem formulation. The global optimality of a scheduling and estimation strategy pair for the unicast network model is established. A person-by-person optimal pair of strategies is obtained for a broadcast network model.