A method for vibrational viscometers capable of high-viscosity measurements using self-excited oscillations is proposed and assessed both theoretically and experimentally. Such viscometers are well-known for their rapid response and miniaturization. Unlike conventional methods based on Q-value estimations obtained experimentally from the frequency response or resonance curve, we describe the use of self-excited oscillations in viscosity measurements using positive velocity feedback control without relying on the frequency response curve. Such measurements become possible even for high viscosities where the peak of the frequency response curve is ambiguous or does not exist, i.e., the Q-value cannot be estimated from such curves. Furthermore, the validity of the proposed method is experimentally tested using a prototype self-excited viscometer. Downsized oscillators such as micro- or nanoscale cantilevers can be self-excited following a straightforward application of the method. They are expected to enable not only localized monitoring of changes in high viscosity with time but also spatial high-viscosity measurements by the distributed arrangement of the devices.