Near field dBM testing

I am far from an electronic mastermind but enjoy hobby ideas and expanding on designs. I am not into radio or remote control circuits but instead I stick to digital and micro-controller design. I developed a couple circuit boards that consist of a shift register and EEprom controlled by an off-board Arduino connected with Dupont wires. The shift register is timing at five mili-seconds and of course generating near field noise,
To start a discussion, I researched FCC compliance concerning unintentional radiators and purchased a Tinysa spectrum analyzer along with near field probes. My question is: Is there anyone who does self compliance testing on their boards and what parameters are looked at. Is it dBm, frequency, etc and what limits are considered satisfactory for a basic unintentional radiator self compliance test. I do have a basic understanding and will stop here to limit the post length.