<p>We study the sensitivity of displaced vertex searches at the LHC to heavy neutral leptons (also known as sterile neutrinos) that are produced in pairs with an electroweak-size cross section. We work within the context of a supersymmetric model in which the sterile neutrino is produced along with Standard Model particles in higgsino decays. By making use of model-independent reconstruction efficiencies provided by the ATLAS collaboration in their search for displaced vertices with multiple jets, we obtain constraints on this model from 139 fb⁻¹ of data collected by ATLAS during the LHC Run 2, and assess the discovery reach of Run 3 and of the high-luminosity LHC (HL-LHC). Depending on the higgsino mass parameter, sterile neutrino masses between 20 GeV and 230 GeV and active-sterile neutrino mixings in the range 4 × 10⁻¹⁴ ≲ <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>V</mi> <mi>N</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {V}_N^2 \)</EquationSource> </InlineEquation> ≲ 3 × 10⁻¹⁰ can be excluded. At the HL-LHC, discovery-level significances could be reached for sterile neutrinos masses up to 295 GeV and values of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>V</mi> <mi>N</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">\( {V}_N^2 \)</EquationSource> </InlineEquation> down to 3 × 10⁻¹⁴. Finally, moving away from the supersymmetric scenario, we study to which extent these results can be generalized to a broader class of models in which the sterile neutrinos are produced in the decays of heavier particles that are themselves pair-produced with an electroweak-size cross section.</p>