Home made loop antennas (or the nice Tekbox set), pin probes, PCB-based antennas (home made or
http://www.wa5vjb.com), TEM cell (Tekbox or home-made
http://www.emcs.org/acstrial/newsletters/summer08/pp2.pdf) are all suitable to solve EMC problems.
Oh and there is a really good LISN design here (I've built a 4channel version) (
https://www.eevblog.com/forum/projects/5uh-lisn-for-spectrum-analyzer-emcemi-work/30/)
However your 30-300MHz area of interest puts some challenges in terms of a convenient antenna size.
Once you have a list (or plot) of frequencies affected i.e. failing and by how much, you have all you need to solve it.
And you may as well pop a 300-400MHz LPF on the front to get rid of all the other spectral stuff you dont care about.
It is a radiated fail? or a conducted?
http://www.compliance-club.com/archive/old_archive/010422.htm (this is for conducted, though its just one part of a series of excellent articles)
Once you have a probe, start sniffing around, you should be able to account for all the spikes you see.
The frequencies you get from the EMC lab may not be 100% correlated to the frequencies you observe so just look in the vicinity.
Take a peak hold measurement sweep/scan at the same or similar RBW as used by the lab. Repeat with an average reading. Between Average and Peak will be the QP (quasi peak value), and peak is ~= lab 'peak' so you should be able to find the source(s).
Be prepared to hack the board to bits, i.e. cut tracks, swap out values, put in CM chokes etc.
Oh and lastly, I have found frequency decomposition useful - what is a potential fundamental of this frequency of concern. Be prepared to look beyond the fail frequency to its harmonics or fundamental...