The reading on a power meter will vary a LOT depending on where the meter sits in the overall total-length of coax cable. To get an accurate reading, the meter MUST sit at an interval of 1/2 wavelength along the transmission line. The only way to easily do this is by insuring that you are using a half-wave input jumper cable on your meter.
Cable electrical wavelength is figured by the Speed of Light (299,792,458 meters per second) divided by the frequency in Hertz, the dividend of which is multiplied by the velocity factor of the cable (look at the specs for the cable you are using).
For instance, if my meter's input jumper was made from RG-213u, I would see that the velocity factor for that cable is 0.66. (sometimes shown as 66%)
(NOTE: In this example, I have used 462.600 in the GMRS band as my desired frequency. 462,600,000 Hz)
Let's do the math: 299792458 / 462600000 = 0.6480597881539127 * Velocity factor of 0.66 = 0.4277194601815824 Meters. That is a full-wavelength of cable, and we need a half wavelength, so cut it in half. So, your jumper cable into the meter should be about 21.5 centimeters long, or about 8.5 inches.
If you were using a smaller cable, like RG-58u with a foam dielectric, which has a velocity factor of 0.535, then you would need .1734 Meter jumper, or about 6.8 inch jumper to correctly match the input of your meter.
If you are using just some random-length input jumper, particularly if it is over a full wavelength long, then you may not be even close to the half-wave point, depending on the length of the rest of the cable going to the antenna, and the meter will not read right. If you use this calculated length of input jumper, accounting for its velocity factor, then whatever is on the output side makes no difference to the reading accuracy.
By the way, this rule goes for SWR meters as well as power meters. If you set up your UHF antenna with a 3-foot truck-stop CB jumper going into your meter, then you are likely WAY out of 'whack'. These rules still apply at HF also. It isn't as critical below 30 MHz since the wavelength is so long, but if you use a 4 or 5 foot long meter jumper at CB frequencies, it WILL be wrong. At 27.205 MHz, use a 6 inch jumper, or else a 9.6 foot one for accuracy.
Tech hint: I keep several different lengths of pre-made jumpers in my Bird watt meter case for different frequency bands that I normally work with, and have them all tagged as to what band range they are for. The higher you go in frequency, the more critical this gets, and the SHORTER they get... sometimes TOO short, thus for 950 MHz, I keep a 15.6 inch jumper of LMR-400, which is 1.5 Wavelengths, but still on a calculated half-wavelength point in the line. A 5.2 inch long LMR-400 jumper is too short to work with.
Long winded, sorry, but I hope this helps.