Considering all our previous experience in the design of new cholinesterase inhibitors, especially resveratrol analogs, in this research, the basic stilbene skeleton was used as a structural unit for new carbamates. Inhibitory activity was tested toward the enzymes acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) by newly prepared carbamates 1–13. In the tested group of compounds, the leading inhibitors were 1 and 7, which achieved excellent selective inhibitory activity for BChE with IC50 values of 0.12 ± 0.09 μM and 0.38 ± 0.01 μM, respectively. Both were much more active than standard inhibitor galantamine against BChE. Molecular docking of the most promising inhibitor candidates, compounds 1 and 7, revealed that stabilizing interactions between the active site residues of BChE and the ligands involve π-stacking, alkyl-π interactions, and, when the carbamate orientation allows, H-bond formation. MD analysis confirmed the stability of the obtained complexes. Some bioactive resveratrol-based carbamates displayed complex-forming capabilities with Fe3+ ions as metal centers. Spectrophotometric investigation indicated that they coordinate one or two metal ions, which is in accordance with their chemical structure, offering two binding sites: an amine and a carboxylic group in the carbamate moiety. Based on all obtained in silico, experimental, and computational results on biological activity in the present work, new carbamates 1 and 7 represent potential selective BChE inhibitors as new therapeutics for neurological disorders.