New micellar coordination clusters (MCCs) were prepared by the introduction of a hydrophobic chelator onto the interface of nonionic surfactant Triton X-114 followed by “crosslinking” of the structures by metal ions. Their resistance to changes in ionic strength, pH of the solution, and temperature was investigated. Regularities in the interaction of MCCs with α-, β-, and γ-cyclodextrins (CD) were revealed. It was shown that the variation of the type and concentration of CD allowed one to control the mechanism of MCC synthesis and to affect their stability. The involvement of molecular modeling (molecular docking) made possible to elucidate the most energetically favorable structures of complexes of CD with components of MCCs.