If your TEM cell has a reasonably good match with 50 Ohms and you manage to position your DUT in the middle, the results will be quite accurate. My own TEM cell's corrections are around 4dB up to 1GHz. You can go down the rabbit hole and getting everything calibrated but unless you invest massive amounts (like >200k euro / dollar) in a shielded / dampened room, your measurements will always be off. So the best approach is to measure relative based on pre-compliance testing at a certified lab. If the lab finds a peak at 200MHz going 6dBuV over the limit and you measure 72dBuV in your test setup, you need to make that 72dBuV drop by at least 6dB. And preferably more. Having test data from a lab also enables you to collect corrections for your own setup.
Near field probes are only useful to get a rough estimate where radiation from a board is coming from. A HF low-Z probe to measure signals directly is a good addition for trying to find sources of radiation. Typically it is a particular trace / node in a circuit which causes emissions at a certain frequency (band).