In this work, a special application of the nuclear resonance fluorescence technique has been used and further advanced to study nuclear structure effects: so-called relative self-absorption experiments. They allow for the direct determination of ground-state transition widths of excited states, an important quantity for comparisons to model calculations, as well as the level width and the branching ratio to the ground state of individual states in a model-independent way. Two self-absorption measurements have been performed. On the one hand, the absolute excitation widths and the decay pattern of low-lying excited dipole states in the energy regime of the pygmy dipole resonance have been investigated in the nucleus $^{140}$Ce. The results of the nuclear resonance fluorescence measurement, which is part of a self-absorption experiment, as well as of the actual self-absorption measurement are presented for 117 and 104 excited states of $^{140}$Ce, respectively. They are compared to previous measurements and discussed with respect to the statistical model. On the other hand, a high-precision measurement of the self absorption of the $T=1$, $J^{\pi}=0^+_1$ level at an excitation energy of \unit[3563]{keV} in $^6$Li has been conducted. A precisely measured level width of this state can serve as a benchmark for modern ab-inito calculations.