  Particles are a widespread tool for obtaining information from fluid flows.
When Eulerian data are unavailable, they may be employed to estimate flow
fields or to identify coherent flow structures. Here we numerically examine the
possibility of using particles to capture the dynamics of isolated vortex rings
propagating in a quiescent fluid. The analysis is performed starting from
numerical simulations of the Navier--Stokes and the
Hall--Vinen--Bekarevich--Khalatnikov equations, respectively describing the
dynamics of a Newtonian fluid and a finite-temperature superfluid. The
flow-induced positions and velocities of particles suspended in the fluid are
specifically used to compute the Lagrangian pseudovorticity field, a proxy for
the Eulerian vorticity field recently employed in the context of superfluid
$^4$He experiments. We show that, when calculated from ideal Lagrangian tracers
or from particles with low inertia, the pseudovorticity field can be accurately
used to estimate the propagation velocity and the growth of isolated vortex
rings, although the quantitative reconstruction of the corresponding vorticity
fields remains challenging. On the other hand, particles with high inertia tend
to preferentially sample specific flow regions, resulting in biased
pseudovorticity fields that pollute the estimation of the vortex ring
properties. Overall, this work neatly demonstrates that the Lagrangian
pseudovorticity is a valuable tool for estimating the strength of macroscopic
vortical structures in the absence of Eulerian data, which is, for example, the
case of superfluid $^4$He experiments.
