Shore fish with a resident license from either Minnesota or Wisconsin where the St. Croix River is a border. NPS/VanTatenhove. Catch something big in the St. Croix River. NPS/Butler. The St. Croix National Scenic Riverway is a great place to fish! Clean water and a wide variety of underwater habitats make for outstanding fishing opportunities on the St. Croix and Namekagon rivers. On the Namekagon River upstream of Hayward, Wisconsin, the cold water habitat has received national recognition for the naturally reproducing brown and brook trout fisheries.