We derive robust, decentralised and scalable stability criteria for networks of heterogeneous systems. Stability of the network is guaranteed if the dynamics of each local area of the network satisfies a globally specified protocol. The results are suitable for a broad class of network models, allowing for interconnection asymmetries, multi-input-multi-output systems and nonlinearities. For networks of single-input-single-output systems with a bipartite interconnection structure the protocol takes the form of a graphical Nyquist type test. This allows local control systems to be designed using loopshaping techniques. In the general setting the protocol take the form of a frequency domain inequality, and design can be conducted using linear matrix inequalities. Vve apply the techniques to construct a protocol for networks of detailed synchronous machine models. This illustrates that the conditions can be used for scalable stability verification and design of high fidelity electrical power system models.