Several new methods for faulted transmission line parameters estimation in phasor and time domain are proposed, that eventually improve the overall performance of numerical distance relays. The concept of dynamic phasors is introduced to accommodate the time-variant nature of the current and voltage signals during transients and faults. Based on dynamic phasor transmission line models, direct and indirect estimation methods are derived. For the proposed indirect estimation method, stability of prediction error dynamics is assured by using the Lyapunov direct method. Presented estimation techniques are compared with a conventional stationary phasor solution as well as with a recursive least-square estimator derived in the discrete time domain. In the evaluation, more realistic assumptions are considered with regards to distortion of the input voltage and current signals along with the variable fault resistance because of arcing faults. Simulation results and actual field measurements are included for performance evaluation of the proposed estimators.