If using wooden skewers, soak them in warm water for 20 minutes before preparing kebabs. Prepare your grill or fire for grilling (we made ours on a grate over our backyard fire pit).
Arrange the skewers beginning with salmon, followed with lemon, then salmon, lemon, salmon. Set aside and repeat with remaining salmon. Season the kebabs generously with kosher salt and freshly ground black pepper.
In a small saucepan, heat the birch syrup and rosemary over medium-low heat. When the mixture just comes to a simmer, remove from heat and brush liberally over the skewers, being sure to coat the lemons as well as the salmon. Reserve any remaining rosemary syrup to brush over the skewers as they grill.
Grease your grill to prevent the salmon for sticking as needed. Place the skewers on the grill over a hot fire, brushing with syrup as you go, cooking until salmon is cooked to medium in the center (or to your preference), and has grill marks on both sides (ours took 2-3 minutes per side, but this will depend on the heat of your fire and the proximity of the skewers to the flame). Drizzle any remaining syrup over top of the skewers and serve promptly.