Networks of weakly coupled oscillators can display complex phenomena of partial synchrony, e.g., chimera states. While some features of the model are conserved in its respective phase-reduced model up to first order in the coupling strength, others require the usage of terms of higher order to be present. Recently, we used the concept of phase-isostable coordinates to derive those terms for coupled two-dimensional limit-cycle oscillators. Here, we use this approach on an ensemble of non-identical Stuart-Landau oscillators coupled pairwisely via an arbitrary adjacency matrix. Ultimately, we arrive at a second-order extension of the paradigmatic Kuramoto-Sakaguchi model for networks and explicitly demonstrate how the adjacency matrix translates into the multi-body coupling structure in the phase equations. To illustrate the power of our approach and the crucial importance of high-order phase reduction, we tackle a trendy setup of non-locally coupled oscillators exhibiting a chimera state. The second-order phase model reproduces the dependence of the chimera shape on the coupling strength. This feature is not captured by the typically used first-order Kuramoto-like model.