How do utilities calculate transmission lines impedance?
Some confusion seems to have arisen between the electronics engineer use of 'impedance' to mean 'characteristic impedance', and the electrical engineer use of 'impedance' to mean 'inductance and resistance of a lumped element'.
Rest assured that it does make sense to calculate 'the impedance' of a 300 kV, 1,000 km transmission line, it's just that the electrical engineers are talking about a different kind of impedance.

I learned how to do distance relay settings calculations in a training course (though I haven't done it for real, yet.) Apart from that, I do power system analysis for a living, so I am familiar with the transmission line impedance calculations.
For overhead transmission lines, we can calculate the impedance (per kilometre) if we know the following:

The type of conductor, i.e. '30/3.00/7/3.00 ACSR/GZ', used for the main circuits and the earthwires (if any). This lets us look up the AC resistance/km and the physical outer diameter of the conductor, which is needed for the calculation.
The spacing of the conductors at the pole top, which determines mutual inductance effects.
The spacing of the conductors above the ground, and the ground volume resistivity, which determines capacitance to ground.

The calculation method can be found in either of the following well-known books:

Westinghouse Electrical Transmission and Distribution Reference Book (now published by ABB). Chapter 3, Characteristics of Aerial Lines.

Areva Network Protection and Automation Guide (freely available online) - section 5.18 Equivalent Circuits and Parameters of Power System Plant - Overhead Lines and Cables.
A lot of useful data is given here, including typical OHL configurations. This book was formerly known as the GEC Protective Relays Application Guide, and is considered the &quot;bible&quot; for British and Commonwealth electrical protection engineers.