Correctly measuring EMI is very complex. Not only do you need the correct spectrum analyzer (special versions are available, called e.g. EMI analyzer; they do measurements in accordance with EMI specific standards). You also need the proper environment and a calibrated set of antennas and an EMI chamber or a free area, with metal floor (very simplisticly speaking; detailled descriptions can be found on the net), or a TEM cell for smaller items. For most hobbyists, the effort goes beyond whats realistically doable.
Overall, measuring electrosmog from a device like a computer, which was certified to CE/FCC anyway, with most of the meters described above, is just not doable correctly. At best, you can get a qualitative overview, comparing e.g. two computers. That is not necessarily very meaningfull. You can have two equal numbers, but one may still be not compliant (having a strong spike at a specific frequency, while the other has the energy broadly distributed). So the bad news is, correctly measuring the EMI of a computer (which is a low level emitter), is complex and expensive.
In theory, if you find a cheap EMI antenna somewhere (i have never seen one, most are 2k up...), you could buy a 8590 spectrum analyzer (going up to 1.5GHz as a cheap solution, you get that below 1k. Not a quasi-peak analyzer, but will do. Move to your backjard which is located somewhere in an area with no EMI emitters around (industry facilities, radio stations...), do a scan without DUT, and do one with the DUT, and compare data. A metal mesh on the ground would be needed. All this is still far away from being standards-compliant, but is not too bad either. Dimensions are important (mesh size...., see information available on the internet). If properly set up, and with a good antenna in a suitable area, this could even be used as a setup for internal precompliance-testing, prior to doing an EMI certification.