I looked at my instructions for my RCBS Charge Master Scale and they recommend running it off a UPS.
This is not, in and of itself, good advice. I must assume that given the course of the thread, that power conditioning is what is being sought in the suggestion of a UPS. One must understand, however, the differences between UPS's.
There are the standby types, and online types. Most of your "Best Buy" bargain UPS's are the standby type. This means that when they sense power loss, they kick their output to battery supplied power in some amount of time (typically 6 milliseconds). They do nothing during normal operation to condition the power being delivered to the load.
The online type feeds conditioned power to the load at all times, thereby controlling the quality of said power at all times. These are not as easy to find, and are more expensive.
It would be substantially more cost effective to just run the unit using batteries.
As for my Rangemaster 750, I just leave it on 24/7. Never had a problem yet.