120 Hz as a test frequency is close enough to 60 Hz to get reasonable results.
The problem when measuring transformer leakage inductance is that you cannot avoid measuring the combined primary and secondary leakages of the transformer i.e. you measure a composite number either referred to the primary (when the secondary is shorted) or referred to the secondary when you short the primary.
To do this you have to apply shorts to the winding you are not measuring. This means that the magnetization inductance is largely removed from the measurement. And, when measuring magnetization inductance you run the opposite winding open circuit so that the effects of leakage inductance are largely not considered when making the measurement.
Because the magnetization inductance is usually at least 20 times more that the leakage inductance, shorting the secondary puts the secondary inductance in parallel with the magnetization inductance and, the number you read is therefore mainly the leakage inductance (because it is so much smaller in value): -
So, for a 1:1 transformer (as an example) if the secondary is shorted, (and ignoring copper losses), \$L_S\$ becomes in parallel with \$L_M\$ and, because \$L_S\$ is around +20 times lower in value compared to \$L_M\$, \$L_M\$ is more or less removed from the resulting number.
Additionally, you only need to do one measurement of leakage inductance because, which ever direction you do it in, it will be a combined measurement of primary and secondary. So, choose a measurement winding and then short the other winding out.
I'm having trouble to simulate transformer models in OrCAD
If I am making a transformer equivalent model in a simulator I try and mimic the full circuit shown above. I cannot say why your model isn't working for you.
Measuring core losses is more problematic because you have to apply full supply voltage to the primary and use a watt-meter.