Checkpoint Levels work fine if all of your character classes have the same XP requirements for each level, and if you don't mind consulting an extra chart. But here's an easier and more widely-applicable method of letting players "save" some of their progress between characters when those characters kick the bucket.
Checkpoints 2: Check Pointier
When a player's first PC dies, they divide that character's experience points in half (rounding down if it's not a whole number) and record that as their "Checkpoint." The next character they create in the same campaign will begin with that much XP, and the corresponding level for their class.
Every time that player loses a character in the same campaign afterward, they divide that character's XP in half as before, then compare it to their current Checkpoint. If it is higher than the Checkpoint, then it becomes the new Checkpoint, and the next character begins play with that much XP. Otherwise, the old Checkpoint remains, and the next character begins with that XP amount. Thus, one's Checkpoint never decreases within a given campaign.
Clarifications and Caveats
If a PC dies, the player of that PC may create a new character within the campaign at any level less than or equal to the equivalent of the player's current Checkpoint. Each player is responsible for keeping track of their own Checkpoint; it would probably be best to write it on their character sheets. Checkpoints do not transfer between players or between campaigns.
A PC can lose levels due to magical "energy drain" or other such in-game effects, but a player's Checkpoint never decreases within a given campaign. For example, let's say Susie loses her first PC, a level 4 fighter, meaning her Checkpoint is 4,000 XP (assuming it's a standard game of old-school D&D). She picks another fighter for her next character, who begins at level 3. Unfortunately, she soon loses a level to the chilling touch of an evil specter, becoming level 2. Susie's Checkpoint remains at 4,000 XP, even if her current PC dies with less experience, so she can still make her next character at a level equivalent to 4,000 XP. Of course, if Susie wants to increase her Checkpoint beyond that, she will still need to play at least one PC who survives to gain at least 8,002 XP.
(Yes, this means that a player could have their level-drained PC rush recklessly into danger specifically to get killed so they can make a new character at a higher level. I personally think that would almost always be incredibly lame, and I probably won't feel bad if the player gets mocked for this, but it is technically allowed.)
By default, each player can only control one PC at a time.* This does not include retainers, henchmen, etc., as they are technically NPCs controlled by the referee (and are simply "ordered around" by a PC unless the referee explicitly allows otherwise), they are created by the referee rather than a player, and they are not subject to the benefits of a player's checkpoint level.
*If a referee wishes to allow multiple PCs per player, they could simply determine a player's Checkpoint based on the highest amount of XP that any of their PCs have ever reached in the campaign, as usual. This could be prone to exploitation, as a player with one PC at a significantly higher level than all of their other PCs could purposefully kill off their lower-level PCs for instant higher-level replacements, and that would be pretty lame. To prevent this, stricter rules may be desired. For example, the referee could allow each player a certain number of "slots" to be filled with living, active PCs, and require each player to track a separate Checkpoint for each slot.