Alissa G. answered 06/29/19
Professional Proofreader/Editor and Writing Coach
Hello! I think that grammatically and historically speaking, the most accurate version is, "I have no pen with which to write." The general rule is that you should not end a sentence on a preposition ("I have no pen to write with"). However, since spoken language is constantly evolving, the fact of the matter is that most native speakers of English tend to be sloppy and break grammar rules often. In speech (as well as conversational writing), most people use the latter of the two versions you have mentioned.
All in all, I would agree that the former, although correct, is generally reserved for formal writing (academic, business, etc.), and that the latter is most commonly used in everyday speech.
I hope that helps!