Believe me, my dear Mrs. Worldly,
Most sincerely yours,
This last is an English form, but it is used by quite a number of Americans—particularly those who have been much abroad.
Appropriate for a Man
"Faithfully" or "Faithfully yours" is a very good signature for a man in writing to a woman, or in any uncommercial correspondence, such as a letter to the President of the United States, a member of the Cabinet, an Ambassador, a clergyman, etc.
The Intimate Closing
"Affectionately yours," "Always affectionately," "Affectionately," "Devotedly," "Lovingly," "Your loving" are in increasing scale of intimacy.
"Lovingly" is much more intimate than "Affectionately" and so is "Devotedly."
"Sincerely" in formal notes and "Affectionately" in intimate notes are the two adverbs most used in the present day, and between these two there is a blank; in English we have no expression to fit sentiment more friendly than the first nor one less intimate than the second.
Not Good Form
"Cordially" was coined no doubt to fill this need, but its self-consciousness puts it in the category with "residence" and "retire," and all the other offenses of pretentiousness, and in New York, at least, it is not used by people of taste.