For the lime mayonnaise, combine all ingredients and salt and pepper to taste in a small bowl and mix well. Refrigerate until needed.
For the salmon- Combine the garlic, lime rind, lime juice, salt and pepper to taste in a large bowl. Rub the salmon with the lime mixture.
Heat butter and oil in a shallow frying pan, add the salmon, flesh side down, and cook until lightly browned. Turn, cook until done as desired Serve salmon with lime mayonnaise and an extra wedge of lime, if desired.