Containerization has emerged as a popular technology for deploying applications in cloud environments due to its lightweight and portable nature. As containers become increasingly prevalent, the need for efficient live migration techniques to support workload balancing, fault tolerance, and resource optimization has become evident. In this study, we investigate the impact and cost of container live migration in the context of cloud computing. Leveraging the capabilities of Amazon Web Services (AWS), we establish an experimental approach by using different technologies of AWS like Amazon Elastic Compute Cloud (EC2), Amazon Elastic Kubernetes Service (EKS), and AWS CloudWatch, to facilitate live migration of containers and tracking its cost implications. Our findings provide valuable insights into the effectiveness and efficiency of container live migration in cloud environments, paving the way for informed decision-making and optimization strategies for containerized workloads in production settings.