This paper outlines a design approach for biomedical wireless power transfer systems with a focus on three-coil inductive links for neonatal intensive care unit applications. The relevant literature has been explored to support the design approach, equations, simulation results, and the process of experimental analysis. The paper begins with a brief overview of various power amplifier classes, followed by an in-depth examination of the most common power amplifiers used in biomedical wireless power transfer systems. Among the traditional linear and switching amplifier classes, class-D and class-E switching amplifiers are highlighted for their enhanced efficiency and straightforward implementation in biomedical contexts. The impact of load variation on these systems is also discussed. This paper then explores the basic concepts and essential equations governing inductive links, comparing two-coil and multi-coil configurations. In the following, the paper discusses foundational coil parameters and provides theoretical and experimental analysis of both two-coil and multi-coil inductive links through step-by-step measurement techniques using lab equipment and addressing the relevant challenges. Finally, a case study for neonatal intensive care unit applications is presented, showcasing a wireless power transfer system operating at 13.56 MHz for powering a wearable device on a patient lying on a mattress. An inductive link with a transmitter coil embedded in a mattress is designed to supply power to a load at distances ranging from 4 cm to 12 cm, simulating the mattress-to-chest distance of an infant. the experimental results of a three-coil inductive link equipped with a Class-E power amplifier are reported, demonstrating power transfer efficiency ranging from 75% to 25% and power delivery to a 500 Ω-load varying from 340 mW to 25 mW over various distances.