The harmonic balance method is a well-established technique for solving the unsteady Reynolds-averaged Navier–Stokes equations for problems that are periodic in nature and the frequencies of the flow features under study are known a priori. This is often the case when investigating problems in turbomachinery where relevant frequencies are, for example, the rotational speed of the shaft or eigenfrequencies of structural eigenmodes of blades . To obtain an accurate time-dependent solution, higher harmonics of these frequencies along with their linear combinations must be included in the simulation. The number of these frequencies taken into account is a parameter that strongly influences both computational costs and the accuracy of the solution. Here we address the question of how to determine the relevant frequencies which have to be included in the simulation in order to achieve an accurate solution in a cost-efficient way. The current approach involves computing an initial solution using a set of frequencies selected on the basis of an educated guess. A subsequent simulation is then performed with an expanded set of frequencies. This process is repeated until adding more frequencies no longer leads to significant changes in the solution, as assessed by changes in integral values or one-dimensional profiles. A more efficient method for determining the frequencies required to obtain an accurate solution is proposed. In this method, the residuals of the harmonic balance equations in the frequency domain are analyzed with a discrete Fourier transform that uses a larger set of frequencies than the harmonic balance algorithm itself. The amplitudes of the Fourier components are then used to identify which frequencies should be added or removed during the simulation. Applications of the proposed method to aeroelastic problems in turbomachinery are presented, showing its efficiency.