The current paper aims at the discussion of the uncertainties of hydraulic transient modelling using the classic method of characteristics and incorporating unsteady friction (UF) and pipe-wall viscoelasticity. A two-stage calibration procedure is used for estimating the model parameters: the first stage refers to the calibration of steady state conditions and the second stage to the transient state. This step-wise calibration procedure, although simple, consists of a set of guidelines useful for engineering practice when having pressure and flow data, instead of the blind simultaneous calibration of all known parameters. A data collection programme was carried out in an experimental facility, composed of high-density polyethylene pipes to collect transient pressure data for different initial discharges. Results obtained have shown that UF and viscoelasticity, despite being phenomena that have completely different natures, have similar effects in the transient pressure response, which the inverse transient solver is not capable of distinguishing.