Methods to measure inductance with high (1%) precision using standard equipment?
The method you use is very error sensitive, ESR can be an issue but also determining the exact voltage ratios isn't easy.

I would use LC-parallel resonance:

\$F_c=\frac 1 {2\pi\sqrt{LC}}\$

Get a 1% (or better) accurate capacitor. If you do not have such a capacitor then just forget about the whole thing, you will not get the 1% accuracy.

Use a circuit like this:







simulate this circuit &ndash; Schematic created using CircuitLab

If you have a rough value for Lx then use the formula above to determine the resonance frequency in combination with the accurate capacitor C_1%.

You should aim for a frequency that the signal generator can easily generate, for example 1 MHz. Set the generator output voltage a couple of volts, the exact value does not matter because we want to determine the resonance frequency.

Vary the frequency of the generator and on the oscilloscope keep an eye on the signal amplitude. The frequency where the amplitude is the largest, that is the resonance frequency. Then use that frequency and the value of C_1% to determine the value of Lx? using the formula above.

If the signal generator is not very accurate (if it is an analog signal generator) then measure the frequency using your oscilloscope. You need a better than 0.01% accurate value for the frequency otherwise you cannot get the 1% overall accuracy. Your oscilloscope is a digital one so it can measure frequencies with more enough accuracy.