You're right, something has been omitted.
These expressions are familiar and much used, but neither is a sentence; neither has a verb. They are so natural and idiomatic that I'm having difficulty thinking what the full sentence form might be
Here are my suggestions.
(I offer) best wishes to the happy couple.
(Here is a gift/card for you) with love and best wishes on this happy occasion.
Those sentences reflect the sentiment of the shorter comments, but I am sure that no one actually thinks those particular words when they write the comments.