Sensitivity and spatial resolution in Magnetic Particle Imaging are affected by magnetic properties of the nanoparticle tracers used during imaging. Here, we have carried out a comprehensive magnetic characterization of single-core iron oxide nanoparticles that were designed for MPI. We used ac susceptometry, fluxgate magnetorelaxometry, and magnetic particle spectroscopy to evaluate the tracer's magnetic core size, hydrodynamic size, and magnetic anisotropy. Our results present a self-consistent set of magnetic and structural parameters for the tracers that is consistent with direct measurements of size using transmission electron microscopy and dynamic light scattering and that can be used to better understand their MPI performance.