The inductance of a loop needs to be measured without any other components connected to it.
Attach the meter to the ends of the loop and wait for the value to settle. If the value is quickly changing over a wide range then squeeze the meter clips tight onto the wire. In some cases there is a signal in the area of the antenna that is causing the value to bounce and the antenna needs to be moved to a quieter location.
The inductance is measured with a 1 kHz signal. To properly measure the inductance the signal should be 134.2 kHz but only expensive desktop inductance meters allow choosing different frequencies. But the 1 kHz value still provides inductance measurements that are close enough for PIT tag antennas.
LCR meters also measure capacitance and resistance. If you are keeping good records you might want to also measure the R. The capacitance C of a loop of wire is not significant.