A nonrestrictive clause offers extra information about something you have mentioned in a sentence, but the information isn’t essential to identify the thing you’re talking about. Nonrestrictive clauses are usually introduced by which or who and should be set off by commas.
The clause “which Chester recommended” is nonrestrictive because “Posey’s Cafe” is already specific. Identifying it as the restaurant recommended by Chester doesn’t narrow it down any further.
The clause “whom I love dearly” is nonrestrictive because you could remove it and it would still be clear that you’re talking about the same person—“my wife” is already specific.