A vibrating wire viscometer formed from a tungsten wire with radius of about 0.125 mm has been used to measure the viscosity of certified reference fluid S60 at temperatures between (273 and 373) K at a pressure of 0.1 MPa where the viscosity varies from (0.0062 to 0.652) Pa s and the resonance quality factor Q lie between (20.8 and 1.02). Our results differ from the values cited by the supplier by less than +/- 3 % over the whole range of Q, T, and p. We have also measured the viscosity of certified reference fluid S20, with eta(293 K, 0.1 MPa) approximate to 37 mPa.s, while stagnant at pressures below 69 MPa and temperature between (298 and 423) K and also while flowing S20 at volumetric rates up to 66 cm(3).s(-1). The values obtained in stagnant S20 differed insignificantly from those while flowing and suggest there is no additional systematic error arising from flow in the viscosity obtained from an axially symmetric vibrating wire viscometer. The working equations for a vibrating wire have been used to estimate Q as a function of viscosity up to 1 Pa.s for wires with radii between (0.05 and 0.3) mm. The calculated Q compares favorably with the observed values and suggests a wire of radius about 0.2 mm can be used to measure the viscosity of fluids up to 1 Pa.s.