The low-valent rhenium(I) salt Na[Re(η$^5$-Cp)(BDI)] (BDI = N,N′-bis(2,6-diisopropylphenyl)-3,5-dimethyl-β-diketiminate) was shown to react with various halide and chalcogenolate reagents, leading to the isolation of a series of rhenium(III)–halide and −pseudohalide complexes: Re(X)(η$^5$-Cp)(BDI) (1-X, X = F, Cl, Br, I; 2, X = OTf) and Re(ER)(η5-Cp)(BDI) (3-ER, ER = SBn, SeBn, TePh). The 1H NMR spectra of these complexes displayed sharp resonances shifted several ppm from typical diamagnetic regions, as well as distinct chemical shift trends down both the halide (with the exception of F) and chalcogenolate series, with both Cp and BDI backbone peaks moving downfield with increasing atomic number. Subsequent magnetic susceptibility measurements of the rhenium(III) halides 1-Cl, 1-Br, and 1-I indicated that these complexes display temperature-independent paramagnetism (TIP), with χTIP values of 7.41(44) × 10$^{-4}$ to 1.50(51) × 10$^{-3}$ cm$^3$ mol$^{-1}$. Multireference complete active space self-consistent field (CASSCF) computations incorporating spin–orbit state mixing revealed small energy separations (1.7–3.0 kcal/mol) between thermally isolated ground states and the first excited spin–orbit states for the rhenium halides, confirming that low-lying excited states are responsible for the observed TIP behavior.