Coppock, Joyce ElizabethI discuss the design and operation of a system for levitating a charged, $\mu$m-scale, multilayer graphene nanoplatelet in a quadrupole electric field trap in high vacuum. Levitation decouples the platelet from its environment and enables sensitive mechanical and magnetic measurements. First, I describe a method of generating and trapping the nanoplatelets. The platelets are generated via liquid exfoliation of graphite pellets and charged via electrospray ionization. Individual platelets are trapped at a pressure of several hundred mTorr and transferred to a trap in a second chamber, which is pumped to UHV pressures for further study. All measurements of the trapped platelet's motion are performed via optical scattering. Second, I present a method of gyroscopically stabilizing the levitated platelet. The rotation frequency of the platelet is locked to an applied radio frequency (rf) electric field $\bm{E}_{\mathrm{rf}}$. Over time, frequency-locking stabilizes the platelet so that its axis of rotation is normal to the platelet and perpendicular to $\bm{E}_{\mathrm{rf}}$. Finally, I present optical data on the interaction of a multilayer graphene platelet with an applied magnetic field. The stabilized nanoplatelet is extremely sensitive to external torques, and its low-frequency dynamics are determined by an applied magnetic field. Two mechanisms of interaction are observed: a diamagnetic polarizability and a magnetic moment proportional to the frequency of rotation. A model is constructed to describe this data, and experimental values are compared to theory.enDissertationPhysicsNanoscienceCondensed matter physics2D materialsDiamagnetismGrapheneIon trapMagnetismNanoparticle