Legendary Resistance (3/day): If the creature fails a saving throw, it can choose to succeed instead.
I dislike this ability. It is not fun at all.
I understand why it exists - because otherwise there are way too many save or suck powers that can easily leave any boss struggling to take a single turn while the party murders them - but giving the boss several Get Out of Jail Free cards per day, with no clear indication to the players that their attack worked and the monster just decided that "Nope, I don't like that!" feels unfair and unfun to me. On a second thought, giving a clear indication what just happened might be worse, as the player just wasted a limited resource and there is not even a trick to be learnt and abused later - it just doesn't work until brute-forced by running the boss out of their daily uses.
Here are d6 alternatives to Legendary Resistance. While this is parlance specific to D&D 5e, these abilities should be easy to use for any OSR boss just as well.
1. Save Immunity: The boss automatically succeeds on any saving throws it is proficient in.
I like immunity on bosses more than resistances. Giving a boss one or two immunities and clearly communicating that to the players gives them a nice restriction to work around, which breed creativity. Giving a boss some resistances basically just prolongs combat.
2. Save Adaptation: The boss automatically fails when it makes a saving throw of each type for the first time, but always succeeds afterwards.
A variation on Save Immunity, this means that the players' powers just work (fun) but cannot keep the boss bound for long (also fun). It also forces the players to change their approach each round - no spamming the same spell over and over. Few fights will take more than 4 or 5 rounds and this power should reset between encounters, so the boss probably won't become immune to everything.
3. Purge: As a bonus action, remove one effect affecting the boss.
This should be a bonus action, so that the boss can use it without giving up its turn completely, but works best if the boss has other bonus actions that will compete for their place in the action economy. You can debuff the boss, but it will rarely last more than a round. Still, it will cost it a bonus action it could otherwise use for more nefarious purposes. Plus if you can layer several effects, or somehow force it to use its other bonus action, you can keep the debuffs going. This is my second favourite, as it gives the GM some fun decisions to make in the heat of combat and at the same time prevents the boss from sucking for long even if it fails every single saving throw.
4. Reflect: When targeted by a spell that allows a saving throw, the boss and the caster roll an opposed ability check. If the caster fails, their spell is redirected back at them.
Very scary power that nonetheless doesn't help if the boss fails and gets caught in whatever nasty spell the wizard had prepared. High risk, high reward.
5. Unfair Exchange: As an action, the boss targets one enemy that must make a saving throw. On failure, the boss and the target exchange all their temporary effects.
The boss tries to switch its debuffs for a PC's buffs. Once again, very scary but dependant on a failed saving throw of the PC.
6. Redirect: As a reaction when it fails a saving throw, the boss can redirect the effect to one of its nearby underlings.
This is pretty close to the original Legendary Resistance, but the players get a clear indication that their power worked, that the boss is evil, abusing its minions like that, and that there is a solution - remove all minions. Also their power still works, if against a minion, so nothing feels wasted. This is my definite favourite.
For extra fun, instead of minions, give the boss several fully independent shadow clones and have it switch places and effects with the clones. Chaos reigns.