This paper reports viscosity data for mixtures containing a refrigerant (HFC-134a) and a lubricant (triethylene glycol dimethyether, TriEGDME, or tetraethylene glycol dimethyl ether, TEGDME), at 12% of TriEGDME or 14% mass fraction of TEGDME. The measurements (140 data points) were obtained at various pressures (between 10 and 140 MPa) in the monophasic liquid state from 293.15 to 373.15 K. Because HFC-134a and the polyethers are not in the same single phase at normal pressure and temperature (the refrigerant is a gas, whereas the polyethers are liquids), accurate measurements of their mixtures require specific procedures for preparation of the samples and filling of the apparatus. A specially designed isobaric-transfer falling-body viscometer is used in this work. The viscosities of the mixtures are, on average, 40% higher than that of the pure refrigerant, and this increase is more noticeable at low temperatures. The experimental viscosities have been used to check the predictive and correlation ability of several viscosity models (mixing rules, Geller and Davis method, self-referencing model, hard-sphere theory, free-volume model, and friction theory). Most of the studied models underestimate the dynamic viscosity values over all of the temperature and pressure ranges investigated.