If using saffron, in a small bowl, stir together the saffron and 2 teaspoons boiling water; let cool. Add the mayonnaise and garlic and stir to combine.
Heat grill to medium-high. In a medium bowl, toss the shrimp with the oil, coriander, and ½ teaspoon salt. Grill until opaque throughout, 2 to 4 minutes per side. Serve with the aïoli for dipping.