At home: Combine vermouth, Benedictine, and bitters in a mixing glass. Stir and funnel into a TSA-approved plastic container. Place container and lemon strips in a quart-sized resealable plastic bag.
On the plane: Order a cognac and have your companion (or a complete stranger, if they are friendly) order a rye whiskey. You want ice, but you want to pour the booze yourself. Divide the mini-bottles between the two cups of ice and split the contents of your carry-on container. Stir with a drink stirrer (fingers work too). Squeeze lemon peel over the drinks, skin side facing down, and enjoy.