Three of the four New Hampshire incumbents were re-elected.
Under New Hampshire law a majority of voters (12.5% of votes) was required for election. Only three candidates achieved a majority, and so a run-off election was held for the fourth seat.
| District | Incumbent | Party | First elected | Result | Candidates | |||
|---|---|---|---|---|---|---|---|---|
| First ballot | Second ballot | |||||||
| Jeremiah Smith | Pro-Administration | 1790 | Incumbent re-elected to a new party. Federalist gain. | nowrap rowspan=4 | First ballot : √ Jeremiah Smith (Federalist) 20.5% √ John Samuel Sherburne (Democratic-Republican) 17.2% √ Nicholas Gilman (Federalist) 13.0% Abiel Foster (Federalist) 11.1% Paine Wingate (Federalist) 8.1% Others 30.1% Second ballot : √ Abiel Foster (Federalist) 82.7% Paine Wingate (Federalist) 17.3% | |||
| John Samuel Sherburne | Anti-Administration | 1792 | Incumbent re-elected to a new party. Democratic-Republican gain. | |||||
| Nicholas Gilman | Pro-Administration | 1788/89 | Incumbent re-elected to a new party. Federalist gain. | |||||
| Paine Wingate | Pro-Administration | 1792 | Incumbent lost re-election. New member elected. Federalist gain. |