Make sure that the short circuit you apply is of low impedance , especially for low-turn transformers. A terminating loop of just a few cm diameter can result in an inductance measurement significantly higher that the internal leakage of the transformer you are trying to measure. Measure dc winding resistances with a four-terminal measurement setup. You can use a simple lab current source and Fluke voltmeter to get very accurate dc measurements. A similar setup with the AP102B frequency response analyzer will produce good results at frequencies up to 1 MHz or more for low resistances.
Leakage inductance is a function of frequency.
Make sure you specify the measurement frequency for both leakage inductance and magnetizing inductance to your manufacturer. For most switch-mode power transformers, a sense resistor of either 0.1 or 1 ohm can be used to extract the needed frequency response data.