However, depending on which options I choose on the Spectrum Analyzer, my measurements are different by up to 6-10 dB(!).
Using a spectrum analyzer needs a bit of understanding what it does: it sweeps a filter across the spectrum and measures the power passing through that filter.
I didn't know how to properly use a spectrum analyzer when I first did, and none of the students I've met did – so, a spectrum analyzer is a mighty tool, that can easily mislead!
For example: Depending on the settings, you might not actually "hit" the tone with the passband center of your filter (and see less energy), or you might have a setting that divides the observed power by the filter bandwidth to give you a power density estimate, or a lot of other settings.
This is the first time I hear of that specific spectrum analyzer – and it's the first measurement device where the specifications are a microsoft word file. It specifies 50 kHz frequency accuracy — that's not really a great frequency standard, so you might be thinking you're tuning right onto the tone, but still be 50 kHz off (by the way, proper spectrum analyzers go through great lengths to more accurately describe the distribution of the frequency error, which is a thing relative to the center frequency – but assuming the spec means a standard deviation of 50 kHz error at 2.6 GHz, we can with a lot of good intentions hope for around 19 kHz at 900 MHz).
At first, I just used a fairly wide span and "Peak Search" which showed me the signal power in dBm. However, the peak search doesn't seem to be very accurate: Repeating with different settings (or just re-pushing "Peak Find") gives different results.
Yeah, sounds like the peak search functionality isn't great.
That might compound with the bad frequency accuracy and the fact that the tuning steps are very rough – a distance between possible frequencies of 100 kHz ("Settings Resolution") makes it hard to properly find the signals you're looking for, and also, if one can only tune in multiples of 100 kHz, the 30 kHz minimum resolution bandwidth means you're missing 70% of spectrum!
So, stay away from that peak-finding tool, and don't use any resolution bandwidth smaller than the tuning steps – that leads to "holes" in your spectrum observation, which the SA then "incorrectly" interpolates with a line.
Interestingly for RefLevel=0dBm and RefLevel=20dBm the results seem somewhat consistent but RefLevel=10dBm is off.
Hm, that sounds wrong. If you don't change anything about the source of your power, i.e. don't move any cables, configure the X310 differently or send a different signal, that would be an indication of a measurement device error, or perhaps of some hidden setting (like an assumed probe attenuation or something).
But, maybe that's all in the tolerances of your system: the spec sheet only says an error of 3 dB (that's a factor of 2!!!) is to be expected within 300 MHz to 2.6 GHz. Wow.
Zooming closely into it, the signal widens significantly due to leakage.
No, that's just the resolution bandwidth of your filter!
Is the method with peak search more accurate or the ACPR measurement (even though I am receiving a pure CW)?
Since there's no point in doing an ACPR in a single-tone test:
No, this all sounds like you really need to learn what a spectrum analyzer does and how to use it – don't fret, there's great tutorials out there.
Any other recommendations when it comes to measuring signal power with a SA?
Generally, start as basic as possible – if you know you're only (or nearly only) emitting a single tone, use a wide filter and a long dwell time.
Use a measurement strategy that uses the fact that the daughterboards of the X310 are generally very linear for long swaths of their gain – see the performance metrics for your daughterboard to see what that range is for your frequencies and gains of interest.
Generally, you'll need a measurement strategy – and that depends on what you want to actually know! It doesn't seem like your interest actually lies in generating tones of a specific power, but probably in more complex signals, so when setting up said strategy, make sure you actually deal with that.
I'd start by using generating a uniformly distributed white noise signal, and passing it through a relatively sharp low-pass filter, so to generate say 10 MHz of band-limited white noise out of 25 MHz Nyquist rate (which is identical to sampling rate, since complex sampling). That's trivial to do with GNU Radio, and you can easily also visualize an average digital magnitude squared of that in GNU Radio; that's the digital domain power of the signal!
So, when you successfully generate that broadband signal somewhere in the avg mag² region of 0.4, you send it using your USRP (the power limitation is a good idea to avoid USRP clipping). Now, you have 10 MHz that contain a known amount of digital power; use the 1 MHz wide resolution bandwidth on your SA, and you'll be able to, without having to think a lot about frequency errors, read the power that you see in that 1 MHz bandwidth; since that's 1/10 of the total power sent by the USRP, you get your physical power per digital power mapping.
But, honestly: Your measurement device's spec are really bad. You'll be better off just using Ettus'/National Instruments performance data measurements, they have less uncertainty than 3 dB.