This paper provides a comparative analysis of kinematic retargeting algorithms for controlling anthropomorphic robotic hands in tasks requiring high dexterity. Three algorithms, namely DexPilot, TeachNET, and BioIK, were evaluated utilising the Shadow Dexterous Hand, a robotic hand with 24 joints designed to replicate human-like movements. Experimental results revealed that DexPilot outperformed the remaining algorithms, offering superior precision, stability, and natural grasping in complex tasks, such as small object manipulation. TeachNET demonstrated competitive performance but fell slightly short of DexPilot, while BioIK faced significant limitations due to instability in the OpenPose hand detection method, responsible for frequent misdetections and consequently reduced accuracy. These findings highlight the strengths and weaknesses of current kinematic retargeting techniques and suggest that further improvements in hand pose acquisition methods, such as motion capture or depth-sensing systems, could significantly enhance robotic hand control in teleoperation scenarios. This study advances the understanding of robotic dexterity and establishes a foundation for future research in human-robot interaction and robotic teleoperation systems.