A torsionally driven cavity, consisting of a fully enclosed cylinder with rotating bottom lid, is used to examine the confined swirling flow of low-viscosity Boger fluids for situations where inertia dominates the flow field. Flow visualization and the optical technique of particle image velocimetry (PIV) are used to examine the effect of small amounts of fluid elasticity on the phenomenon of vortex breakdown. Low-viscosity Boger fluids are used which consist of dilute concentrations of high molecular weight polyacrylamide or semi-dilute concentrations of xanthan gum in a Newtonian solvent. The introduction of elasticity results in a 20% and 40% increase in the minimum critical aspect ratio required for vortex breakdown to occur using polyacrylamide and xanthan gum, respectively, at concentrations of 45 p.p.m. When the concentrations of either polyacrylamide or xanthan gum are raised to 75 p.p.m., vortex breakdown is entirely suppressed for the cylinder aspect ratios examined. Radial and axial velocity measurements along the axial centreline show that the alteration in existence domain is linked to a decrease in the magnitude of the peak in axial velocity along the central axis. The minimum peak axial velocities along the central axis for the 75 p.p.m. polyacrylamide and 75 p.p.m. xanthan gum Boger fluids are 67% and 86% lower in magnitude, respectively, than for the Newtonian fluid at Reynolds number of Re ≈ 1500–1600. This decrease in axial velocity is associated with the interaction of elasticity in the governing boundary on the rotating base lid and/or the interaction of extensional viscosity in areas with high velocity gradients. The low-viscosity Boger fluids used in this study are rheologically characterized and the steady complex flow field has well-defined boundary conditions. Therefore, the results will allow validation of non-Newtonian constitutive models in a numerical model of a torsionally driven cavity flow.