This article discusses the problem of exceeding amplitudes of mistuned structures caused by accelerated traveling waves type excitation, i.e., traveling waves with time variant frequencies. These waves cause resonance passages of, e.g., rotating structures. To calculate the resonance passage a semi-analytical solution is proposed. Thus, high accuracy is guaranteed. The topic of exceeding amplitudes is initially approached by studying a discrete lumped mass model with detuned parameters. It can be shown that under certain circumstances the maximum amplitude of the transient resonance passage is even higher than the maximum amplitude of the steady-state solution. To investigate this phenomenon on a real bladed disk, the number of degrees of freedom of the blisk is reduced using component mode synthesis (CMS). By applying the semi-analytical solution to the reduced model, the envelopes of the vibration during resonance passage can be calculated. Processing extensive parametric studies it can be pointed out under which circumstances the probability rises that higher maximum amplitudes occur during resonance passage compared to steady-state conditions.