Fourth Edition does not have a real saving throw mechanic. The narrative concept represented by the saving throw has mostly been replaced by the three extra defenses: fortitude, reflex, and will. For example, rather than rolling a save vs. poison when a poisonous attack hits a character, instead a monster would roll an attack against the character’s fortitude defense.
There is something called a saving throw in Fourth Edition, but it does not have the same game role (4E PHB page 279). Instead, it is a way to throw off a status effect (and thus support temporary effects that do not require bookkeeping). It’s a clever innovation, but it’s not a saving throw as traditionally understood. A 4E save has a 55% chance of success (10 or higher on a d20), unaffected by level or ability scores (a strange choice for a game that supports such heavy character optimization, but there it is). There are a few ways that an attacker can make saves against their status effects more difficult (like the orb of imposition wizard implement effect), but they don’t seem to be very common. And again, they are on the side of the attacker (condition becomes harder to shake off) rather than on the side of the defender.
This is unfortunate, because I like the level-dependent saving throw mechanic. It is impervious to PC build optimization. It rewards smart play by making characters that are able to survive harder to kill. I could just import the saving throw tables from a previous edition, but that would be confusing to my players and would overload the meaning of saving throw. So I decided to create a new mechanic for the Nalfeshnee Hack that serves the same function. It is called the luck throw.
The luck throw is a DC 16 check with a one-half level bonus. A roll of 1 is always a failure. Thus, at first level, there is a 25% chance of success (16, 17, 18, 19, 20). Chance of success increases with level, until at level 28 (+14), failure only occurs on a 1.
The luck throw is appropriate for any last chance escape possibility where you don’t want to base success on an ability score. Abilities in 4E tend to extremes (lots of 18s and 10s, because of their effect on powers), making them a bad fit for last chance mechanics (some PCs are almost always going to make an ability check while others are only going to make it sometimes). I imagine this problem is true for any version of the game that overemphasizes ability scores (really, AD&D on). (See here for more discussion about using ability scores for saving throws.)
This seems to be a reasonable approximation of the traditional saving throw mechanic. It is a simple formula, so it is easy to remember, and it also fits the feel of other Fourth Edition rules. It is similar to the Swords & Wizardry single saving throw, though it does not vary by class.