Passing Saves/Hitting on a Natural 1

[Cogidubnus]

Are there any ways to pass saves and hit enemies on a natural one if your modifier is large enough.

[Zaydos]

There are some class features that let you pass saves even on a natural one.

A knight's 17th level ability

Steadfast Determination makes them not be auto-failure for Fort.

Some abilities let you reroll nat ones on saves.

[cylch]

In ToB there's maneuvers in the diamond mind discipline that allow you to use Concentration for saves and don't auto fail on a roll of one. I forget their names at the moment

[KillianHawkeye]

If you are a deity with a Divine Rank of 1 or higher, you do not automatically fail if you roll a 1 on your attack rolls or saving throws. Greater deities (Divine Rank 16-20) always take the maximum value of any die they roll.

[Sdonourg]

Some luck feats can do it.

[dextercorvia]

Among other things, Divine Rank 1 confers the ability to not miss/fail on a 1.

Edit: Ninja Dieties.

[Tyndmyr]

Are there any ways to pass saves and hit enemies on a natural one if your modifier is large enough.

The answer to your question is luck feats.

There's a luck feat that lets you treat a Nat 1 on a save as a Nat 20. While it's powered by luck points, it's clearly superior to the other methods of removing the nat 1 = auto fail, because it provides a benefit even when the DC is high.

There's also a luck feat to reroll attacks. I realize this isn't the same as ignoring 1s, exactly, but 1/400 odds are pretty slim. It becomes a very worthwhile feat when DMs use crit charts.