Approve, commend and approbate can be used to suggest formal praise or consent.
Approve is the most informal of these words and is also used generally. When used officially, it means to consent or confirm.
Ex – Your proposal has been approved by the government.
Commend is more formal than approve and is always used in an official context. It means to praise as worthy of confidence, notice etc.
Ex – He was commended for doing a remarkable job as the leader of the team.
Approbate is the most formal of these terms. It is usually used in its noun form. It means to approve officially.
Ex – His report was approbated by all members of the council.