Alternatives to using a nut: use a cheese-head or socket-cap screw wound down till the head meets the surface. Or a bolt rather than screw: tighten it to the thread run-out then measure across the un-threaded shank.
In either case, measure both inside and outside distances and find their mean.
Using the mill as Bill suggests is fine but you don't need a DRO to be able to do it. Use the hand-wheel dial but make the table's last movement to register in both holes, in the same direction as that for moving to the second hole.
Similarly with the caliper: it does not matter if that is of vernier or digital type. The method is the same.
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Occasionally I find myself having to measure across two holes too far apart for any high-precision instrument I own, though this is usually where reasonably wide tolerances are acceptable. Forced to use a rule, I do not try to estimate placing the rule level with the centres by eye, but measure to the edges of the holes. Right-hand on both, left-hand on both; calculate the mean.
For measuring some parts of my steam-wagon, the firm-joint calipers and rule are all I have.
I used to see one or two of my superiors at work trying to measure by rule between centres estimated by eye. I tried to persuade them that measuring across like edges is easier and more accurate. Unfortunately I lacked the right Ologies in Computerese, Physics and Ropey English, so had no more success there than teaching them that for a row of matched items, "at xx mm pitch" is both correct and shorter than "at xx mm centre-to-centre distances" ! Luckily the nearest mm was appropriate, and often the best obtainable .