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Hi,
I think you should add a load (something that draws a good amount of current but is within the transformer's rating) and then measure. Short-circuit testing could damage the transformer and open-circuit testing might not give the exact result.
Open circuit, primary and secondaries, will give an approximate indication that the core material is correct if ungapped (+/-30%) and the number of turns are also correct again (+/-30%). In the case of a gapped core it should be more specific.
Short circuit as suggested by others will give an indication of leakage inductance. That will give you an indication that the device has been wound according to your specifications if you reference it against a known good device.
The above would probably be done with a 'bridge' where current levels would not be an issue.
If you wanted to verify turns ratios and phasing then you would probably be driving the primary, at an appropriate sine wave frequency, and making measurements referred to the primary, probably with an oscilloscope, on the secondaries.
Under those circumstances as Tahmid suggests you would have to load the secondaries to some level to ensure realistic results.
If the core was gapped, as would be the case in a flyback transformer then the above method would not give a true indication of turns ratios but would still allow you to check phasing. Open circuit testing in the gapped case should ascertain that the actual turns are correct.
I see a tendency to complicate things more than necessary. In fact, an open circuit measurement should be sufficient to determine the exact windings ratios and also magnetziation current, magnitude and phase (respectively losses). Short circuit measurement is another standard measurement for power transformers. Of course it will not damage the transformer, because it's performed with a reduced primary voltage at the nominal current. The expectable transformer voltage drop due to windings resistances and leak inductance is derived from the short circuit measurement. In my opinion, the measurement methods form eletrical power engineering can be more or less transfered to high frequency transformers.
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