Difficulty getting good ripple / noise measurements

You could use the FFT of your RTM3004 to see if there is a revealing pattern.

That certainly helped get a better picture of what was going on. A spectragram revealed some intermittent noise around the ISM band here in the UK - 433MHz and just under 700MHz. I think that's to be expected. However, the big reveal was a lot of noise around 20MHz that disappeared when I went out into the garden. I suspect this is the USB power built in to my wall outlets. I also remembered that I was using an old-ish Ethernet over poweline adapter but that didn't seem to be causing any problems.

However I still have a fair amount of noise at lower frequencies. The FFT says arounf 76kHz but I think that'll be a rough figure. I'm still not sure what this is, but it's still swamping any readings I'm getting from the PSU.

76kHz is a common frequency for PFC and PMIC.

A 20 MHz peak seems to be high for switch mode supply harmonics. Maybe an artifact generated by a PC?

When I was testing this:  Building a Low-Cost Low-Noise Negative- or Positive-Rail Power Supply 

I was getting ballpark 40 MHz noise coming from somewhere. I never managed to get to the bottom of it : (

In my case I could power from a battery and put it all in a metal box, but I don't have any ideas for when the DUT is the power supply itself : ( maybe an isolation transformer powering the supply could partially help if that noise is coming from the mains, but maybe it wont have much improvement : ( Or, a mains filter (example one is mentioned here:  Building a Mains Breakout Box ) . Or, add a load of ferrite beads to the output wires of the power supply (using coax). I don't think it's unreasonable to use the ferrite on the supply output cables for the roadtest, I think that's a very valid way to use the power supply. And any customer buying the R&S supply for the low noise, would love to know which ferrites/how many of them, and how to wire up to the circuit under test, using whatever cable Fred27 decides on and measures with. Would be super-useful to all I reckon, even those with other power supplies.

Regarding ferrites any of these might be good: farnell order codes 1838839 or 1651719  or  1703107, or even fatter ones (and pass the wire through a couple of times at least, and maybe use many of them, e.g. three or four at least.

n.b.: industry convention for noise measurements is 20 MHz. Many oscilloscopes have a "high-bandwidth/20 MHz" switch because of that. 

Jan Cumps said:

A 20 MHz peak seems to be high for switch mode supply harmonics. Maybe an artifact generated by a PC?

Notches roughly where the amateur bands are suggests HF PLC (either video or networking).

https://rsgb.org/main/blog/news/special-focus/pla-plt/2012/11/12/a-standard-for-powerline-telecommunications-devices-the-rsgb-involvement/

"So in simple terms what does this mean? The standard has been approved and devices that fail to meet it will no longer be able to be sold, after a three-year grace period, unless certified to meet EN50561-2012. Significant protection is provided for the Amateur HF bands, as the standard specifies fixed notching for these and other safety of life bands, reducing conducted emissions from PLC devices to the levels of EN55022."

Jan Cumps said:

A 20 MHz peak seems to be high for switch mode supply harmonics. Maybe an artifact generated by a PC?

Notches roughly where the amateur bands are suggests HF PLC (either video or networking).

https://rsgb.org/main/blog/news/special-focus/pla-plt/2012/11/12/a-standard-for-powerline-telecommunications-devices-the-rsgb-involvement/

"So in simple terms what does this mean? The standard has been approved and devices that fail to meet it will no longer be able to be sold, after a three-year grace period, unless certified to meet EN50561-2012. Significant protection is provided for the Amateur HF bands, as the standard specifies fixed notching for these and other safety of life bands, reducing conducted emissions from PLC devices to the levels of EN55022."