Mew is far and away the best Baton Passer in the game. It learns every TM in the game, allowing it to pass any type of boost it wants. By using a combination of Rock Polish and either Swords Dance or Nasty Plot, Mew can easily and quickly prepare any offensive Pokemon for an extremely deadly sweep. After a few turns with Mew preparing on the field, you can watch your opponent's team crumble under the sweeper you have turned into an offensive juggernaut. Bring Mew in on a double KO, or into something that cannot do too much damage to it, like Forretress, or something that it can Taunt, such as Wobbuffet, and use Rock Polish while they switch out. When the new counter comes in, you can either boost Attack or Special Attack if you can live through an attack, or just Baton Pass off if you are in killing range, as +2 Speed is much better than nothing.
The EVs on this set give you the most bulk possible in Mew's Special Defense stat, while also giving it a healthy amount of Speed. After a Rock Polish, Mew will even outrun a +Speed Deoxys-S with max Speed EVs, making Mew a speedy threat and giving it the ability to boost its stats or Taunt quickly. Lum Berry is also helpful, as it prevents Mew from being paralyzed or put to sleep, which would end its chances of passing boosts. You can then Taunt your enemy to prevent him or her from trying to status you again. If you wish to make Mew faster, give it a Timid nature instead, and change its EVs to 252 HP / 36 SpD / 220 Spe. This allows you to hit 320 Speed without a Rock Polish boost, which outspeeds neutral natured Latias, Latios, and Lugia, as well as max Speed Rayquaza. After a Rock Polish, you can outspeed Choice Scarf Darkrai and Taunt it to prevent it from using Dark Void. Leftovers is another possibility over Lum Berry, but it is generally not recommended. The recovery granted by Leftovers is helpful, but not nearly as helpful as recovery from status. If you go with Leftovers, you will need to predict every status move and use Taunt, or else Mew will fail to pass its boosts well.
Baton Pass Mew is not a Pokemon who you can just tack onto your Ubers team. It requires a team to be built around it, forming a very deadly Baton Pass team, with all of its teammates playing a very strategic role.
A dual screen supporter is very appreciated to have on Mew's side. Reflect and Light Screen bolster Mew's defenses, and allow it to take more hits before Baton Passing out, meaning it can give the recipient more boosts, making a sweep much easier. A dual screener should obviously be able to set up both screens, which requires bulk, and must also provide the means to get Mew in with little to no harm. The most prominent dual screeners in Ubers are Mewtwo, Latios, Latias, Uxie, and Bronzong, each of whom has its advantages and disadvantages. Mewtwo is a very solid option, as it fulfills many of the above requirements, and is usually your best choice, unless it is your Baton Pass recipient. Mewtwo can Taunt any attempts to Taunt it, as its high base 130 Speed is one of the fastest in the tier. Furthermore, it is quite bulky, and after it sets up the screens, it can Self-Destruct which simultaneously damages your opponent and provides Mew a free switch in. Bronzong can work similarly, with Explosion over Self-Destruct and Hypnosis over Taunt, and is bulkier, but at the cost of it being quite slow, and therefore easy to Taunt, which completely halts your strategy. Both Latias and Latios also have access to Reflect and Light Screen, and both have their pros and cons. Latias is bulkier, and therefore can last longer to set up the screens, and also has Wish to heal Mew when it comes in. Latios is somewhat frailer, but it can use Memento, which lowers your opponent's Attack and Special Attack by two stages, making Mew come in almost unscathed. Both Latias and Latios however, are weak to extremely common moves in Ubers, such as Ice-, Dragon-, Ghost-, and Dark-type moves. Uxie has the advantage of being quite bulky, giving it time to set up the screens, as well as having Memento to ease Mew in switching in. Although it may seem like Uxie is inferior to Latios, it is quite a bit bulkier than Latios and is also not weak to Ice- and Dragon-type attacks, but at the cost of being slower, and therefore easier to Taunt. However, Uxie does have access to U-turn, making it able for it to U-turn out of Taunters and even Wobbuffet, which is another distinct advantage that it has.
In choosing an attacking Pokemon for Mew to pass boosts to, you must first decide whether you want to make it focus on physical or special attacks. There are many more choices for special attacking Ubers than physical attacking ones, making it easier for you to choose a Pokemon who tailors to exactly what you need. However, there is no central physical wall, unlike Blissey for special attacks, meaning physical Pokemon generally have a slightly easier time powering through a team. This Pokemon must also be able to have the ability to hit many, if not all, Ubers for at least neutral damage with 4 moves.
Should you choose to go for a physical recipient, Groudon is by and large the best choice. By using a moveset of Earthquake, Stone Edge, Dragon Claw, and Fire Punch, Groudon can hit every Pokemon in Ubers for at least neutral damage. It has a massive base 150 Attack stat, as well as tremendous bulk on the physical side. After +2 to both its Attack and Speed, Groudon will plow through anything that is not immune to its STAB Earthquake, even the deadly Wobbuffet, and it can use the rest of its moves when your opponent sends out a Pokemon who is immune to it. Furthermore, Groudon is immune to Thunder Wave, making it far harder to cripple. The only Pokemon not OHKOed are heavily defensive, such as other Groudon or Giratina, and thus cannot do much back. It is suggested that you use a Lum Berry on Groudon so it is not burned by Giratina. Rayquaza is another possibility if you wish to eschew bulk for power. Rayquaza has a more powerful STAB Outrage at its disposal, along with mixed capabilities, allowing it to break physical walls more easily.
If you choose to use a special recipient, the best choices are Dialga, Mewtwo, Palkia, or Kyogre, the best of whom being Dialga. All of these Pokemon have high Special Attack and a varied movepool to hit many targets for a lot of damage. Dialga excels above the others, however, because of its larger bulk. Dialga with a moveset of Dragon Pulse, Flamethrower, Thunderbolt, and Aura Sphere hits many targets both powerfully and reliably, especially since you will most likely not have weather support. Furthermore, it has a very handy resistance to Extreme Speed, which bypasses all your Speed boosts, and can end your sweep and you Baton Pass strategy. Lum Berry is still recommended, as Dialga is threatened by Thunder Wave, which will completely cripple it. Mewtwo, Palkia, and Kyogre are all still possibilities, but you must be extremely wary of Extreme Speed.
To complete your Baton Pass strategy, you should have a "cleaner". A "cleaner" is a final sweeper who cleans up the remains of your opponent's team, should your Baton Pass sweeper be killed. You can choose to make your "cleaner" use the same type of attacks (physical or special) or a different type of attacks, and there are pros and cons to each. By choosing another sweeper of the same specialty in attacking, you have another choice to Baton Pass off to, in case your primary sweeper cannot be used, for whatever reason. Also, in the event that Mew has sustained little damage, it can come back into play to possibly pull off a second Baton Pass. On the other hand, by using a "cleaner" who uses the other type of attacks, you can let it sweep, as its counters will be taken out by your main sweeper. For example, Groudon with boosts can easily take out Blissey, which can help out a final sweeping Dialga, should Groudon get KOed. A good choice for a physical "cleaner" is Rayquaza. Its huge base Attack stat allows it to deal a lot of damage even when its only boost is its own Swords Dance or Dragon Dance. Furthermore, it also has Extreme Speed to pick off weakened enemies. For a special "cleaner", Mewtwo is a great choice. Its high Speed and Special Attack stats, along with Calm Mind, make it easy for Mewtwo to devastate a weakened team.
Wobbuffet can also be used with Mew, as Shadow Tag combined with Encore allow Mew to get into play easier. Furthermore, its Safeguard helps not only Mew, but also your Baton Pass recipient, continue its piece of the strategy even when faced with sleep or paralysis status, or after its Lum Berry has been used.