We report on the design, construction, and use of axisymmetric magnetic traps for levitating diamagnetic particles. The magnetic traps each consist of two pole pieces passively driven by a neodymium iron boron (NdFeB) permanent magnet. The magnetic field configuration between the pole pieces combined with the earth's gravitational field forms a 3D confining potential capable of levitating a range of diamagnetic substances, e.g., graphite powder, silica microspheres, and gallium nitride (GaN) powder and nanowires. Particles trap stably at atmosphere and in high-vacuum for periods up to weeks with lifetimes largely determined by choices made to actively destabilize the trap. We describe the principles of operation, finite element design, approximate closed-form results for design rules, and examples of operation of such traps.