For me, I do it this way:
First, I will compare the open string to the 'chimed' octave harmonic over the 12th fret. This is mostly a check to see if I'm 'in the neighborhood' as far as saddle placement.
But then, the real check for me is to then compare the note fretted at the twelfth fret with that same open harmonic: I'm playing fretted notes (except when I'm lazily backsliding and playing country on open E's and A's . . . .) all the time. And depending on your action, it can make a difference. If you check this on a bass that has a pretty high action, that fretted twelfth and the octave harmonic twelfth will read slightly sharp or flat in comparison.
I occasionally get really fussy and compare against the next octave up as well just for grins. Much past that, the relentless IC logic of most tuners begins to butt up against the vagaries of tempered-tuning, and I don't want to flirt with OCD, so I stop before I get too freaked about it.
Admittedly, 'real close' is enough for a lot of situations on a bass playing low, single notes, but it can get messy quick on a guitar playing chords.
I got chapter and verse about this when I played for several years with a steel player who had perfect pitch. He could pick out whoever was 'out' on the bandstand, and rightly felt if he could keep a pedal steel 'right' all night long, we should be able to as well.
Three cautions:
Only do this with brand-new, just installed strings.
And remember that even though the new Brand X strings you're trying out are also roundwound and exactly the same guages as the Brand Y you just took off, you need to do this again: They will read out differently. You can only skip this if you are replacing same with same, on an axe that's already adjusted for them.
And third, always tune UP, never go sharp and let the key down to 'in tune': It will usually keep slipping a bit more. Tuning up tends to 'set' it much better.
J o e y