Using a Spectrum Analyzer (zero span mode, trigger = video, RBW = 1MHz) connected to a calibrated dipole antenna.
Have to search for the Base Station TX channel (925MHz to 960MHz or 1805MHz to 1880MHz).
Usually power sent by a cell phone is difficult to measure because:
1) TX level is function of power received from local cell.
2) you don't know the pattern of the antenna.
3) power is impulsively modulated.
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I suggest to perform an approximate measurement; measure absorbed DC current, the TX power cannot be higher than absorbed DC power.
Also you know that efficiency may be into 25 to 50 % range, so you'll be able to give a rough estimate of TX power with a uncertainty bar of 3 dB
For this particular application to measure the radiated power, using the Spectrum Analyzer and a calibrated vertical dipole antenna, is more than enough.
It will give the radiated power in that particular location. For a better accuracy shall be done multiple measurements (and average), at different wavelengths distance.