Near-field probes can be used to measure electromagnetic fields around a device, so that electrical noise and electromagnetic radiation in general can be investigated.
Such probes can be connected to oscilloscopes or (more frequently done, but also more expensive: I don't have one yet) spectrum analyzers, and field strength and frequencies can be measured.
Commercial probes can be quite expensive (thousands of Euros for a set of passive or active probes, the latter containing an RF amplifier), so for a start, I am considering building my own.
There are some resources about EMI probing and building probes for that purpose on the web. Links to information I have found to be used in my probe building: