The resonance frequency, stiffness, and damping of a structure with screws, bolts, or rivets is strongly influenced by the nonlinear interaction of connected faying surfaces. During the design phase of built-up systems, those system properties and their uncertainty must be understood to meet vibroacoustic design criteria. However, the frictional interaction of fastened joints is poorly understood, and hypotheses are still being made in an attempt to explain the causes of damping in fastened joints. Friction models that do exist either require onerous methods or are overly simplistic. To provide measured data to support future model development, this research uses experimental modal analysis and a time-domain approach to track damping via the ringdown of a pair of plates with a fastened joint with varying applied torques. Amplitude-dependent plots of the loss factor for several modes are provided, which represent the system better than their single-value counterparts. Frequency decrements due to increased fastener torque were less than one-half of a percent in the presented modes. Counterintuitively, increasing fastener torque in the experiment increased the loss factor and slightly reduced the resonance frequencies of the presented modes. Loss factors vary by 67-96%; in the case of the second mode, loss factor depends heavily on vibration amplitude.