Huh, well then I don't know where 1GHz+ comes from -- regular PDN stuff basically runs out at 100MHz or thereabouts, where pin inductance dominates, even for BGAs (which have onboard bypass for this reason). Which means probing is a heck of a lot easier, just, say, tack on a piece of coax to a convenient footprint and use a nice stack of ferrite beads on the cable to deal with ground-return inductance (which isn't perfect, remember there's trace/via inductance from the pad to the plane).
And power supply (control loop) stuff rolls off in the 10s to 100s kHz, and most PDN action (cutoffs/resonances) in the low MHz, easy to probe.
Planes can resonate into the GHz as suggested in the OP, but perhaps there is another way to measure this, besides direct measurement at component pads.
How about... if it's just passive behavior of the PCB and network, excepting devices -- the PCB itself (stuffed with chip passives, but nothing bulky like tantalums or electrolytics; which could perhaps be substituted with resistors for the test?), could be placed inside a stripline jig, and any resonances in the board will register as notches in the stripline's passband.
The stripline would be like, a modest width ribbon of copper foil/braid/PCB stock, strung between two BNC jacks inside a low metal box. Adjust the box height, strip width, and strip end taper, to get close to 50 ohms or whatever, either when loaded with a test item or unloaded, whatever the case may be. Obviously you can't account for any width/length of test board, you'll have to factor that out somehow. Anyway, slide the board around, under the stripline, watching how the passband changes. There should be a few dips/peaks corresponding to reflections off the leading and trailing edge of the board; these will change position as you rotate the board (thus making a longer diagonal chord across it, or spanning the long/short side if it be rectangular, etc.). As you slide the board lateral to the strip, you should see peaks and dips corresponding to PCB structures; any that may be particularly objectionable, in terms of radiated emissions, should show up as a sharp notch in the response.
This will tend to miss resonances that aren't coupled well to external fields: say an internal trace makes a stub length, and only via's to a single pad on the surface. It's internal, so that stub is shielded by planes -- it could have a fairly high Q, or couple into internal waveguide modes*, and be missed in this test. Well, the argument is that it's not going to be an emissions problem; whether it's a functional problem, you'll have to make a special-case test, probably with whatever components connect to that structure. And hey, maybe it's intentional (e.g. buried stripline filters), who am I to judge?
*Mind, these are very low impedance, due to the narrow spacing between planes and dielectric constant; and the Q isn't great, due to FR-4 being the dielectric. It does exist though, so for example it's a good excuse to stitch or bypass planes together reasonably frequently, and more-or-less randomly over the board rather than making a grid pattern (which selects waveguide modes). Or bypassing only locally at loads. Which, to be clear, a random pattern isn't going to prevent modes, it just randomizes them. Presumably that gives better statistics... but it would be cool to actually see a model proving whether that's actually helpful or what...
So, I have no idea if this is actually a test anyone does, or has thought of before; the finished-product version is a TEM cell. This is just a localized partial-assembly level test, on the same premise.
And, I'm thinking s12 (transmission) would be the way to go, but it really shouldn't be much different with the far end terminated, and reading just s11 (basically, backscattering).
And, it could be done with pulses instead (TDR), in which case you might miss the high Q notches/peaks as a few pixels of ripple, but that might be valuable for other reasons, say checking continuity of planes, coupling or damping of signal traces, etc.
Signal traces, right, you'd have to replace most components with representative driving resistances. Well, that's probably why this isn't a thing, huh...
Tim