There is no sense to measure current in the antenna. This is because there are at least two currents in the antenna and they are flowing in opposite direction. It means that your measurement will depends on exact space locaction and frequency, just because your measurement will depends on all currents sum at the point of measurement.
Technically, current or Voltage measurement doesn't have physical sense for the antenna, just because impedance distribution over space in the antenna is very complicated and two different points of antenna will have different current and different Voltage.
Also note that there are at least two sine currents (or even more) in the wire which are flowing in opposite directions, so Voltage and Amperage depends on exact points which you selected for measurement.
All it means that Amperage or Voltage measurement doesn't have any sense for the antenna. It's like measurement of Amperage or Voltage in a very complex circuit by tapping your probes at random point of the circuit. Measured value will depends on exact point and doesn't represent overall current or Voltage in the circuit
You're needs to measure power instead of Voltage/Amperage, just because Voltage/Amperage proportion depends on the environment impedance at specific point of space. So, you're needs to measure power flow which doesn't depends on environment impedance.
There is also no sense to measure power at near field region of antenna which is about one wavelength, but also depends on actual physical dimensions of antenna. This is because your measurement will suffers from reactive fields in the near field region of antenna. In other word your measurement equipment will have inductive or capacitive coupling with antenna. It's like your equipment is connected through capactior or inductor at some random point of your antenna and affects your antenna properties. So, measurement will depends on the exact space location, signal frequency and cannot represent actual antenna properties because it affects antenna configuration.
If you want to measure how antenna radiate electromagnetic waves, you're needs to perform measurement in the far field region, which is at least one wavelength away from antenna. Because there is no antenna directivity effect in the near field region and because there is capacitive or inductive coupling with antenna in the near field region.
In order to measure field strength in the space, you can use simple antenna and some logarithmic detector in order to cover high dynamic range of signal power.
When you keep your measurement antenna in the far field and within environment with constant electromagnetic properties (for example air) you can normalize your measurement to get density of power carried by electromagnetic waves across the surface in the space.
For example +10 dBm/cm2 means that there is +10 dBm power flow through 1 cm2 area of space.
As you can see, Amperage or Voltage doesn't have sense for antenna.
But if you're still wants to research what happens in the near field of antenna (at distance closer than about one wavelength), then you're needs to measure electric and magnetic flux density separately. In such case you're needs to measure Volts per meter for electric field or Amps per meter for magnetic field. This is not so simple, because environment impedance in the near field region of antenna has very complicated configuration and your probe needs to be small enough in order to see flux density distribution over space and to avoid significant influence on antenna properties due to inductive or capacitive coupling.