You need to link the courses together, following the instructions here: https://www.unh.edu/it/kb/article/mycourses-cross-list-combine-course.html
For the most part, Honors courses are part of the Discovery Program, and require approval by the Discovery Committee. They usually have lower caps than general-level courses (usually 20-30 students). They hold students to higher expectation than ordinary courses, and should be conducted in a highly participatory way (e.g. discussions rather than lectures). For more information about forms of Honors Discovery courses, see this page: http://www.unh.edu/honors-program/honors-discovery
Honors courses may also be created at the upper level to serve Honors in Major students. This is relatively rare, as few majors have enough Honors students to fill a section. However, it may be feasible in cases where a single course serves multiple majors (such as GEN 604H, Principles of Genetics), or for general skills and topics (such as research methods or thesis prep).
For information, see the Request for Proposals: https://www.unh.edu/honors-program/request-proposals-honors-symposium-development
The University Honors Program offers oversight and assistance.
Honors Liaisons recruit students for Honors in Major, offer guidance about curriculum, ensure that program information is available and up to date, certify Honors Designations, and certify completion of the program for graduating students.
The first is to be a member of the University Honors Program, which is invitation-only. To see how students are invited, visit this page: https://www.unh.edu/honors-program/admissions . In general students need to become members in the Freshman year.
The second way to participate is Honors in Major, which students generally begin in the Junior year. The requirements and processes to join vary by major. Students should contact their major's Honors Liaison to discuss joining Honors in Major.
See a list of liaisons and requirements here: http://www.unh.edu/honors-program/requirements-contacts