What are Hard-tail Bridges?

Hard-tail bridges are pieces of hardware often seen on solid body electric guitars. They combine bridges and saddles in such a way that the intonation and string action (height over the fretboard) can easily be adjusted post-install. These styles of bridges are best known from Fender’s Stratocaster™ electric guitars.
Because of how they are made, hard-tail bridges work best when used with magnetic pickups (the sort seen on solidbody electric guitars) as opposed to piezo-style pickups. They help with achieving a professional intonation, maintaining a nice low string action, and increasing sustain (due to their solid metal construction).

Some hard-tail bridges also include openings for pickups such as Fender-style single coils and humbuckers. The basic versions just have the bridge and saddle components.
Although they are best known for use on solid body electrics, hard-tail bridges also work great for cigar box guitars. There are now 3 and 4-string varieties available, which make them even more suitable for electric cigar box guitars that have magnetic pickups.