To make the best-grilled salmon, you have to know which side to grill first. There are two rules two remember about making grilled salmon. Cook your grilled salmon skin side down, flesh side up. Cooking fish skin side down is excellent for two reasons 1) the skin side is the presentation side. 2) The skin acts as a non-stick aid against the grill grates. Your skin will get crispy, but your salmon will not be ruined or overcooked if they stick to the grill grates.To make the best-grilled salmon, you have to know which side to grill first. There are two rules two remember about making grilled salmon. Grilling salmon flesh side on a greased grill grates over leads to sticking, and we don't want our salmon sticking to the grill.