Coaxial cable is distinctive in the world of cables in that it is actually one hollow cylindrical cable with a normal wire cable in the middle, separated by a nonconducting insulator core. Testing for power actually requires that you test each wire in the cable separately, as you would with any two wire cable. The only real difference is that you must be careful not to touch the other wire accidentally with your testing probes.
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Screw one end of the coaxial cable into a powered cable or satellite box. The box must be on when you test or else the multimeter will not detect any power, as it only works on live circuits. The nut on the coaxial cable just spins onto the threads of the cable port by hand, do not use a wrench as the torque could damage the delicate audiovisual circuitry.
Turn the multimeter dial to voltage and check that it is turned on. Plug the red prong probe wire into the red voltage port and the black prong probe into the black voltage port. The ports will be on the face of the multimeter.
Place the black prong probe on the middle wire of the probe, as far in as you can get without the probe touching the side walls. Place the red prong probe on the tip of the middle wire and read the voltage reading off the multimeter. Write down this number, so you do not forget it.
Place the black prong probe on the outside surface of the nut on the end of the coaxial cable and the red prong probe on the inside surface of the nut. Read the voltage reading on the multimeter. Write down this number, and you will have the power that is running through your coaxial cable.