Smoke and salt go very well together—just ask any dad with a Big Green Egg. Though you’ll usually find the flavour combination in some sort of barbecued meat, it’s equally stellar in a martini.
A dirty martini made with a splash of olive brine is a particularly good candidate for a little smoke. You could smoke the glass by setting a piece of wood on fire, or you could rinse the glass with a little smoky scotch, which is much easier and little more elegant. The hint of campfire flavour from the booze will add another layer of dimension to the somewhat kitschy cocktail, complementing the funky olive juice without over powering it. It tastes better, is what I’m saying.
Obviously you’ll need a peaty scotch for this, but you’ll only need a little. Just pour a spoonful in the (chilled) coupe or martini glass, swirl it around a bit, then dump it out (perhaps into your mouth, so as not to waste). Make your dirty martini however you usually do, then strain it into the scotch-scented vessel. Enjoy your fully actualised dirty martini, and repeat if needed.