We present a search for long-lived Higgs portal scalars (HPS) and heavy neutral leptons (HNL) decaying in the MicroBooNE liquid-argon time projection chamber. The measurement is performed using data collected synchronously with the neutrino beam from Fermilab's Main Injector with a total exposure corresponding to 7.01×1020 protons on target. We set upper limits at the 90% confidence level on the mixing parameter |Uμ4|2 ranging from |Uμ4|2<12.9×10-8 for Majorana HNLs with a mass of mHNL=246 MeV to |Uμ4|2<0.92×10-8 for mHNL=385 MeV, assuming |Ue4|2=|Uτ4|2=0 and HNL decays into μ±π pairs. These limits on |Uμ4|2 represent an order of magnitude improvement in sensitivity compared to the previous MicroBooNE result. We also constrain the scalar-Higgs mixing angle θ by searching for HPS decays into μ+μ- final states, excluding a contour in the parameter space with lower bounds of θ2<31.3×10-9 for mHPS=212 GeV and θ2<1.09×10-9 for mHPS=275 GeV. These are the first constraints on the scalar-Higgs mixing angle θ from a dedicated experimental search in this mass range.