Games like Button Button Up!
Games like Button Button Up! include Celeste, Webbed, Öoo, Braid, and LIMBO. We matched them by the tags players give Button Button Up! on Steam (Sokoban, 2D Platformer, Puzzle Platformer, Puzzle, and Parkour): closest matches first, and among equally close ones the better-known games.

Celeste
Shared: 2D Platformer · Difficult · Platformer

Webbed
Shared: 2D Platformer · Puzzle Platformer · Cute

Öoo
Shared: Puzzle Platformer · 2D Platformer · Puzzle

Braid
Shared: Puzzle Platformer · 2D Platformer · Puzzle

LIMBO
Shared: Puzzle Platformer · Puzzle · Platformer

Human Fall Flat
Shared: Puzzle · Puzzle Platformer · Funny

Rain World
Shared: Difficult · Platformer · 2D Platformer

Pikuniku
Shared: Puzzle · Cute · Indie

Baba Is You
Shared: Puzzle · Sokoban · Difficult

Planet of Lana
Shared: Puzzle Platformer · 2D Platformer · Puzzle

Defy Gravity Extended
Shared: Puzzle Platformer · Puzzle · Platformer

Squishy the Suicidal Pig
Shared: Puzzle Platformer · Puzzle · Platformer

Portal 2
Shared: Puzzle · Puzzle Platformer · Platformer

Super Meat Boy
Shared: 2D Platformer · Difficult · Platformer

Pizza Tower
Shared: 2D Platformer · Platformer · Funny

I wanna be the Creator
Shared: Puzzle · Platformer · Difficult

ElecHead
Shared: Puzzle Platformer · Puzzle · Platformer

PICO PARK
Shared: Puzzle Platformer · Puzzle · Platformer

SANABI
Shared: 2D Platformer · 2D · Action

ANIMAL WELL
Shared: Puzzle · Puzzle Platformer · Platformer

CATO: Buttered Cat
Shared: Puzzle Platformer · Puzzle · Cute

Spelunky 2
Shared: 2D Platformer · Platformer · Difficult

FEZ
Shared: Puzzle · Platformer · Puzzle Platformer

Toki Tori
Shared: Puzzle · Platformer · Puzzle Platformer