approbation
Official approval or praise for something someone has done.
Approbation means approval or praise, especially official or formal approval. When a teacher gives her approbation to your science project, she genuinely approves of your effort and results and recognizes their value. When a committee grants its approbation to a new policy, it's formally endorsing it.
The word carries a sense of authority and seriousness. You might seek the approbation of your parents before making a big decision, or a young artist might work hard to earn the approbation of an experienced mentor. Getting someone's approbation means they actively support what you're doing and think it's worthwhile.
The opposite is disapprobation, which means disapproval or criticism. If your soccer coach shows disapprobation when players goof off during practice, she's making clear that their behavior isn't acceptable.
While you can use simpler words like “approval” or “praise” in everyday conversation, approbation appears frequently in formal writing and classic literature, so knowing it helps you understand more sophisticated texts.