You will want to book your flight as early possible. Historically, Essence Festival is held every 4th of July weekend. Therefore, pricey holiday fares are in effect by default. Fares will continuously go up as you get closer to the weekend.
First: If you aren’t playing around and want to book your flight to New Orleans NOW! (recommended). Use the Cheapflights.com widget below.
Second: If you are not ready to buy your flight yet, set a price alert on Skyscanner.com or download the mobile apps (Android/iOS). They will check prices regularly and email you if they change.