In The Witch of Blackbird Pond, what was Nat's punishment?
You might find it useful to refer to the specific part of the novel that your question pertains to. This section of the novel comes in Chapter 19, when Nat so gallantly and bravely returns to rescue Kit from being tried as a witch. He brings Prudence with him who shows everyone how Kit taught her how to read. Of course, it is when Goodwife Cruff has her revenge against Kit spoilt that she turns it onto Nat:
"That man!" she shrilled. "Isn't he the seaman? The one who was banished for setting fire to houses? Thirty lashes they promised him if he showed his face here again!"
Although Nat manages to slip away before they capture him, his willingness to show up and defend Kit to see justice done against the ignorance of the community shows what kind of man he is and demonstrates both his love of Kit but also his love of justice.
Because Nat "illuminated" William's house, (lit candles in pumpkins and put them in the windows), Nat's punishment was posted on the Meeting House door. He and his two fellow sailors were locked in the stocks in front of the Meeting House where people mocked them, jeered at them, and threw dirt at them. Then they were banished from the colony. If they were seen in the colony again, they would suffer 30 lashes.