Mind, there is no "one" way to measure an inductor.
Any circuit you can make, in which the impedance of the element in question is sensible at the input, output or both, can be used, given appropriate calibration (or the circuit and given values).
Consider these simple methods:
https://www.seventransistorlabs.com/Calc/RLC.htmlL/C by divider assumes an ideal reactive component in the divider, and based on the ratio measurement (can be done with any AC voltmeter that reads the driven frequency accurately enough), tells what L or C that would be, given the assumption.
I normally use this when I want a crude measurement of a component, letting R = generator impedance (50 ohms) and adjusting F until drop is in the 10-90% range.
Vector impedance, is basically the same thing, but with a series resistor added (we ignore source resistance because it's measured as reference; this requires a simultaneous measurement, and hence the extra resistor), and using a low distortion sine wave, and the scope's phase measurement function, we get a more accurate value -- also we know unambiguously not just what reactance it is, but its resistance as well; at least to within measurement error: the phase measurement tends to be pretty rough (+/- degree or two), so for element phase near 90° (note, that doesn't mean measurement phase near 90°, it's less due to the modest divider ratio!), resistance is proportional to phase difference from 90° and it can easily be measured near-infinite, or negative. (Note that, for electrical purposes, real numbers are a ring, i.e. there is a continuum from positive-infinite to negative-infinite numbers. So this is expected behavior.)
Frequency and Q factor, is practical when measuring higher impedances, and at select (tuned) frequencies. Because the inductive reactance is canceled out with capacitance, the resistance can be measured accurately, and at a chosen frequency F <= SRF. Note that, for very high impedances (large divider resistance, small capacitance), and high frequencies, probe impedance itself is a concern, but for modest values at 10s of MHz or below, a typical 10x probe is generally fine.
Note that we can measure Q both ways, i.e. by resistor divider and by fractional bandwidth. I didn't bother writing a calculator for that, but simply noting the frequencies where amplitude is 70.7% of the peak, and dividing center/peak frequency by that difference, gives the same value. Same give or take -- if the network is more complex than assumed (repeated/overlapping poles at the frequency, or the resonance of a continuous structure like a transmission line), the methods might differ, which is useful info about the network/element itself, though how one might use this difference, depends on the network.
Capacitance by difference, is adding a tweak and measuring the shift in frequency. I probably use this most often when measuring switching circuits, the ringing frequency of a stray oscillation I want to dampen. First introducing a plain capacitor Cx, I determine the in-circuit capacitance; then I use >2C, plus a resistor R = Zo, to dampen the oscillation (which gives a Q factor under 2 or so).
Matching capacitor, is as it says in the description; I use it to measure high-Q inductors at level. Taking careful measurements, using high-Q capacitors (C0G are practically ideal, they are very good capacitors indeed), I get values as accurate as the measurements themselves. So, repeatable within some percent, which is enough to see the effect of, say, bits of metal near an airgap in a ferrite-cored inductor.
The above-posted methods are variations on this (or these) approach(es), with parallel or series arrangements instead. The flanking-capacitors motif effectively swaps series and parallel resonances, so instead of an input dip you see an output peak, etc. The capacitors skew the response -- reactance is lossless, you don't get a straight-up / naive resistance divider, it's impedance, and the transfer curve contorts as a result. Ultimately, all we're doing is rotation and translation on the Smith chart; so as long as we haven't completely lost visibility of the test component (which is guaranteed when lossless components are used around it), we're just picking what frequency we want to measure the element at, and what range of impedance it will present to our instruments at that frequency.
Tim