Improved and novel prediction methods are described for single-phase and two-phase flow of non-Newtonian fluids in pipes. Good predictions are achieved for pressure drop, liquid holdup fraction, and two-phase flow regime, The methods are applicable to any visco-inelastic non-Newtonian fluid and include the effect of surface roughness. The methods utilize a reference fluid for which validated models exist. For single-phase flow, the use of Newtonian and power-law references are illustrated. For two-phase flow, a Newtonian reference fluid is used. Focus is given to shear-thinning fluids. The approach is theoretically based and is expected to be more accurate for large, high-pressure pipelines than present correlation methods, which are all primarily based on low-pressure, small-diameter pipe experimental data.