The dynamic viscosities of four high-viscous vacuum oil samples, working liquids (BM-1CM, BM-1CN, LEYBONOL LVO 500, and Alkaren-D24) for diffusion vacuum pumps, have been measured over the temperature range from 298 to 443 K at atmospheric pressure. The measurements were made using a newly designed rheoviscometer based on falling-body and capillary flow techniques. A new design of the rheoviscometer can be used to measure the viscosity of high and extra-high-viscous working liquids (Newtonian) and rheological properties (non-Newtonian liquids) at low temperatures (near the melting temperature). The present design of the rheoviscometer has some advantage over conventional viscometers. For example, it allows us to measure the viscosity of high and extra-high viscous liquids (Newtonian) and rheological properties of non-Newtonian liquids by changing the shear stress. The combined expanded uncertainty of the viscosity, atmospheric pressure, and temperature measurements at the 0.95 confidence level with a coverage factor of k = 2 is estimated to be U-r(eta)= 2.8%, U-r(P) = 0.01, and U(T) = 0.02 K, respectively. For verification of the reliability, accuracy, and correct operation of the newly designed rheoviscometer, the viscosity of the same oil samples were measured using a conventional well-known capillary flow viscometer over the temperature range from 293 to 366 K at atmospheric pressure. The measured viscosity data for vacuum oils were used to estimate physical meaning parameters of the modified (extended) Arrhenius-Andrade and Vogel-Tamman-Fulcher (VTF) models. The derived VTF parameters (Band T-0, delta = B/T-0) were used to estimate the values of the glass temperature for studied vacuum oil samples.