If you see empty ice cream containers on the table, sprinkles littering the ground, and a can of whipped cream in the trash, you can surmise what happened: someone made sundaes. To surmise is to form an opinion or make a guess about something.
If you surmise that something is true, you don't have much evidence or knowledge about it. Near synonyms are guess, conjecture, and suppose. You might say, "I can't even surmise what he would do in such a situation." Surmise came to English from the French surmettre, "to accuse," which is formed from the prefix sur-, "on, upon," plus mettre, "to put" (from Latin mittere, "to send").