Let's suppose someone asks you about their age. E.g.
(A) What do you think? How old I am?
(B) You seem to be maximum of 35.
(A) Wow! Exactly. How did you say that?
(B) I said it...........
- out of conjecture
- by guess
To me, no one of the above choices sound natural. First because the my spellchecker marks the adverb "conjecturally" as an incorrect one, then based on Ngram shows that the self-made term "by guess" is used very rarely.
So please let me know what is the most natural way to indicate that you say something out of a guess / conjecture?