Swaddle Blankets New babies love the comfort and closeness that swaddle blankets can give them. The comfort can not only help them sleep better, benefitting both you as a new mother and your baby, but can also protect them from scratching their face while they sleep. By wrapping them in a muslin swaddle blanket, you both will see the benefits and importance of keeping your baby wrapped up tight. As they grow, you can find baby swaddle blankets that allow minimal movement, allowing them to transition into sleeping without the swaddle on. For babies with sensitive skin, there are also organic swaddle blankets, helping your baby stay healthy and safe.