Calixarenes functionalized with two catalytic bisimidazolyl-Cu(II) centers and two additional hydroxymethyl (2-Cu2) or aminomethyl groups (3-Cu2) were synthesized as models for enzymes that cleave phosphate diester bonds. The kinetics of 2-Cu2 and 3-Cu2 in the catalysis of the intramolecular transesterification of the RNA model substrate 2-hydroxypropyl-p-nitrophenyl phosphate were compared with those of the parent calixarene 1-Cu2, lacking the two additional functional groups. Under neutral conditions, all complexes show high rate enhancements due to the cooperative action of the Cu(II) ions. The kinetics indicate for 3-Cu2 bifunctional catalytic effects. At the pH optimum of 7.4 at least one amine is protonated, which can assist as a general acid in the binding and activation of the substrate.