The viscosities of microcrystalline cellulose dissolved in 1-ethyl-3-methylimidazolium acetate (EMIMAc) and in 1-butyl-3-methylimidazolium chloride (BMIMCI) were studied in detail as a function of polymer concentration and temperature. The goal was to compare the flow of solutions, macromolecule hydrodynamic properties in each solvent, and the activation energies of viscous flow. Intrinsic viscosities were determined using the truncated form of the general Huggins equation. In both solvents cellulose intrinsic viscosity decreases with increasing temperature, indicating the decrease of solvent thermodynamic quality. The activation energies for both types of cellulose solutions were calculated. For cellulose-EMIMAc the Arrhenius plot showed a concave shape, and thus the Vogel-Tamman-Fulcher (VTF) approach was used. We suggest an improved method of data analysis for the determination of VTF constants and demonstrate that cellulose EMIMAc solution viscosity obeys VTF formalism. Once the dependences of Arrhenius activation energy and VTF pseudo-activation energy were obtained for the whole range of concentrations studied, they were all shown to be described by a simple Power-law function of Polymer concentration.