A method and device are described for making in situ measurements of the density and viscosity of downhole fluids at subterranean wells. An oscillator circuit is deployed in the well comprising an amplifier, a feedback loop, and an electromechanical resonator. The electromechanical resonator is a component in the feedback loop of the oscillator circuit, and has a resonance mode that determines the frequency of the oscillator circuit. The electromechanical resonator is also in contact with the fluid such that the density and viscosity of the fluid influence the resonant frequency and damping of the resonator. The frequency of the oscillator is measured by a microcontroller. In one embodiment, the oscillator circuit periodically stops driving the electromechanical resonator such that the oscillation decays and the rate of decay is also measured by the microcontroller. The density and viscosity of the fluid are determined from the frequency and rate of decay of the oscillation. This measurement technique provides a faster response time to fluid changes than is possible with conventional measurement methods, and the fast response time opens up new applications for downhole viscosity and density measurements, including determining PVT characteristics, phase diagrams, and flow rates.