This thesis describes magnetic measurements of two-dimensional mesoscale superconductors. First, we use a local magnetic probe to directly measure the superfluid response of the tunable, gate-induced superconducting state in MoS₂. Our measurements suggest that disorder strongly impacts the superconductivity in this material, and in some devices we find signatures consistent with a Berezinskii-Kosterlitz-Thouless transition. Our work is described in a manuscript which has been accepted for publication in Nature Communications. A preprint is available on the arXiv (2209.11800). Next, we use magnetic measurements to study the formation and behavior of vortices in ultra-thin, mesoscale disks of MoS₂ and epitaxial NbN. We observe changes in the magnetic response of the disks even with magnetic field much smaller than the critical field. Specifically, we observe sharp dissipative and paramagnetic features near the superconducting transition which are periodic in applied field. We construct a simple model which suggests that transitions between vortex states are responsible for these features. At lower temperatures, we observe a reduction in the strength of the diamagnetism as magnetic field is applied. Finally, at even lower temperatures, the diamagnetism becomes magnetic field independent. The reduction of diamagentism with applied field suggests that vortices are mobile in NbN substantially below T_c, and the restoration of field-independent behavior at lower temperatures is consistent with these mobile vortices transitioning into a frozen state where they no longer decrease the magnetic response of the superconductor. Manuscripts describing these efforts are in preparation.