The management of congestion within the German electricity transmission network has become more important during the last years. This emerging relevance is caused by the increase of renewable generation and the partial phaseout of nuclear power plants. Both developments yield a change in the transmission flow pattern and thus the need for congestion management. Currently, four German transmission system operators (TSOs) are in charge of managing congestion using curative methods, particularly re-dispatch of power plants. However, the existence of four TSOs within Germany induces the question whether coordination between them in managing national congestion would be beneficial. To address this issue, we apply a generalized Nash equilibrium model to analyze different degrees of coordination, covering the German electricity market with a detailed representation of the generation and network structure. Our results indicate that the costs of congestion management decrease in a rising degree of coordination as TSOs take into account congestion in other operators' zones. Total costs are highest in case each TSO is solely responsible for its own zone, and lowest if one integrated entity is in charge of mitigating congestion. We conclude that, in a setup with multiple TSOs, inducing coordination, for instance through a common market, has the potential of lowering the overall costs of congestion management.