It depends on the privilege. Often, an apology is sufficient to resolve a situation. There has been no imprisonment since 1913. There are not many examples we can use to answer the question.
In terms of the question of privilege, the public debate is sufficient to let the people involved know that bad things have been done and that all other punishments have been ruled out. There is no very effective penalty that can be imposed on people.
For example, there are lobbyists. The Office of the Commissioner of Lobbying is responsible for lobbyists, not the House of Commons or the committee. What are we going to do with the lobbyists: are we going to talk about contempt and demand apologies to the House of Commons? It isn't up to you to impose punishment on lobbyists.