Magnetization dynamics are strongly influenced by damping, namely, the loss of spin angular momentum from the magnetic system to the lattice. An "effective" damping constant αeff is often determined experimentally from the spectral linewidth of the free induction decay of the magnetization after the system is excited to its nonequilibrium state. Such an αeff, however, reflects both intrinsic damping as well as inhomogeneous broadening that arises, for example, from spatial variations of the anisotropy field. In this paper, we compare measurements of the magnetization dynamics in ultrathin nonepitaxial films having perpendicular magnetic anisotropy using two different techniques, time-resolved magneto-optical Kerr effect (TRMOKE) and hybrid optical-electrical ferromagnetic resonance (OFMR). By using an external magnetic field that is applied at very small angles to the film plane in the TRMOKE studies, we develop an explicit closed-form analytical expression for the TRMOKE spectral linewidth and show how this can be used to reliably extract the intrinsic Gilbert damping constant. The damping constant determined in this way is in excellent agreement with that determined from the OFMR method on the same samples. Our studies indicate that the asymptotic high-field approach that is often used in the TRMOKE method to distinguish the intrinsic damping from the effective damping may result in significant error, because such high external magnetic fields are required to make this approach valid that they are out of reach. The error becomes larger at lower intrinsic damping constants and thus may account for the anomalously high damping constants that are often reported in TRMOKE studies. In conventional ferromagnetic resonance (FMR) studies, inhomogeneous contributions can be readily distinguished from intrinsic damping contributions by studying the magnetic field dependence of the FMR linewidth. Using an analogous approach, we show how reliable values of the intrinsic damping can be extracted from TRMOKE in two distinct magnetic systems with significant perpendicular magnetic anisotropy: ultrathin CoFeB layers and Co/Ni/Co trilayers.