Viscosity measurements of [xCH4 + (1 − x)C3H8] with x = 0.8888 are reported for temperatures between (203 and 424) K and pressures between (2 and 31) MPa using a vibrating wire viscometer clamped at both ends and operating in a steady-state mode. Reliable operation over this range of conditions required a detailed set of calibration and validation measurements using pure reference fluids. Most previous viscosity determinations with vibrating wire instruments have determined the important vacuum damping parameter Δ0 from a single measurement and assumed it was temperature independent. Here we extended the calibration procedure beyond measurements in vacuum and helium (to determine the wire radius) to include low density methane (ρ ≤ 1.2 kg·m−3) from (223 to 420) K. Using viscosity values for these reference fluids linked to ab initio calculations revealed Δ0 had a temperature dependence below about 350 K, increasing from 2.04 × 10−5 at 372 K to 5.79 × 10−5 at 223 K. Subsequent validation measurements with pure N2 He and CH4 at pressures to 30 MPa confirmed the estimated standard relative uncertainty in viscosity of less 2.5%. The binary mixture measurements were compared with literature data and the predictions of four models including two corresponding states based approaches (ECS and ST), a semi-theoretical model (VW) based on an extended hard-sphere scheme derived from the Enskog equation, and a model (LJ) based on molecular dynamics simulations of Lennard Jones fluids. The ECS and ST models exhibited systematic relative deviations from the data of up to −5% at 150 kg·m−3 and –10% at 300 kg·m−3, respectively. The LJ and VW models provided far better (<4%) representations of the data over their entire range, with the VW model able to represent all the measurements within 3%, which is comparable to their experimental uncertainty.