It comes down to tools and/or technique.
There are a dozen or more ways to accomplish the task. At one extreme is to buy or make a dedicated tool that largely eliminates the need for skill and technique. At the other extreme is to use a common, simple, multi-purpose tool, but use it well, which requires skill and technique.
One dedicated tool is this one, a specialty tool at nearly $200:
One common, simple tool is this one, available at any hardware store for $10:
The first requires relatively little skill or technique to achieve repeatable results: the second requires considerably more skill and technique to achieve repeatable results. There is lots of ground in-between.
One simple, relatively common method is to use a "shooting board" with a sandpapered straight edge. Lee Valley makes all of the components for a formal shooting board, including a track for the sander (or plane), but it is easy to scale that down to make one for just a few dollars, suitable for just nuts and saddle sanding.
Here is Lee Valley's version of their "shooting sander", from which you'll get the idea:
To make your own inexpensive version, apply 80 grit sandpaper to any straight edge - a short level, a block of wood, the edge of a piece of MDF/plywood, etc. You can make a simple bench hook (
https://en.wikipedia.org/wiki/Bench_hook), similar to that shown in the video, from a few scraps of MDF and a few screws. Technique-wise, don't "scrub" the sandpapered straight edge back and forth as doing so will tend to curve the bottom of the saddle/nut. Instead, sand on the push, only.
There are numerous other ways to accomplish the same task, used individually or in combination. After trying many of them, I find this to be simple, effective and repeatable, particularly since I already had the shooting board, track and sander for other woodworking purposes. Thought I'd share the idea/application, though it isn't unique to me or even my invention.