For years I have used the Korg LCA-120 which customizes the notes so you can actually adjust for harmonic tuning of the E, A, D, & G. (E adjusted 2 cents higher, A at 440 Hz, D adjusted 2 cents lower, and G adjusted 4 cents lower.) It also has focus tune which, if turned on, focuses the total range of +-50 cents to a total range of +-10 cents once you get within 10 cents of the correct note. (BTW the way, the difference between a chromatic and harmonic perfect fifth is actually 1.95 cents).
THE PROBLEM IS THAT THE LCA-120 is now obsolete, but you can still find them on the market. I have not been able to find a substitute brand that does as good a job.
Having tuned with the LCA-120 for years, I can not say enough about how it has improved my playing. When I buckled down to superior intonation it was a God send.
The reason is the modern strings are very stable, especially the D'dario Zyex strings which once broken in will stay in tune within a cent, sometimes for days. (ironically it is then the steel E string that is the least stable.)
The main benefit is that if you tune this carefully every time you practice, your fingers can be trained more consistently because you can depend on the exact same placement on the strings for a particular note over a period years.
Those that are willing to listen carefully to one's own playing will find a way into really excellent intonation. The more careful you listen for the nuances the better your intonation will become habituated to precision. I have been taught by a student of Itzhak Perlman to know every half step and whole step of every piece and strictly apply the knowledge to calculate how to get to every finger placement and every shift, and then vigilantly and consciously focus and refine the correctness and relaxation of each all of the time during practice, and move this into mind/body connection (which is the exact opposite of stage fright which is blockage between mind an body) by using the trick of being "all ears" to the notes you are about to play. When you do this right, you will find your body will quickly learn to place your fingers correctly before the next note is played.
BTW really good intonation will not be heard as really good intonation, it will be heard as beautiful sound.