For a transmission line:
Z0 = SQRT( L' / C' ) where: L' = inductance per meter (H/m) C' = capacitance per meter (F/m)
Take a known cable length l. Leave the far end open-circuit. Measure the capacitance between center conductor and shield:
C′= C_measured / l
Short the far end. Measure the inductance seen from the near end. For a shorted transmission line at sufficiently low frequency:
L' = L_measured / l