In The Witch of Blackbird Pond, Nat is, in fact, actually punished in Chapter 16, well before the aforementioned threatened punishment (Chapter 19). He is one of "a rowdy band of rivermen from a trading ship" that comes running into Whethersfield on All Hallows Eve to vandalize the house of the man Kit has been seeing (William Ashby) by placing "lanterns . . . made out of pumpkin heads, with candles inside, and unholy faces cut in the sides to show the light," which Kit's own uncle declares "the devil's invention" with much solemn disapproval. Furthermore, the so-called "rowdy band" stole the pumpkins out of a field to turn them into the jack-o-lanterns.

For those very crimes, on "Thursday Lecture day, the day of public punishment" later that week, Kit slips out and goes alone to the Meeting House, where she finds three men from the Dolphin, Nat's father's ship, in the stocks. Nat, of course, is one of the three, apparently unable to stay out of trouble, even indirectly, at least where Kit or the law might be concerned. The rest of the punishment, aside from time in the stocks (which brought along with it the public derision, scorn, and even abuse of passersby), includes "a fine of forty shillings each" and the reproof to never set foot in Whethersfield again, lest they be whipped (see the threat mentioned in Chapter 19).

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.