Ideas for a high school science fair project involving electromagnets include building a motor, creating an Inductrack system, or experimenting with an electromagnetic propulsion concept. The Inductrack utilizes permanent magnets arranged in a Halbach array to achieve levitation over coils, although sourcing or constructing the coils can be challenging. Other suggestions involve using a car stereo amplifier to power a DC motor, which can create sound effects, or exploring the use of liquid metal that is magnetic. Safety precautions are advised when working with electromagnets, as they can become hot. Overall, projects can range from simple motor constructions to more complex electromagnetic systems, depending on the student's skill level and resources available.