We present and analyze our experimental results on teleportation of two-qubit maximally entangled Bell states on the NISQ (Noisy Intermediate-Scale Quantum) five-qubit processors IBM Q Burlington, Essex, London, Ourense, Rome, Santiago, Vigo and Yorktown. The main obstacle in practical implementation of quantum algorithms on the NISQ computers is caused by hardware errors which depend on the depth of the underlying circuit and its gates. We suggest several modifications of the original teleportation protocol to optimize the depths of its circuit and the connectivity of hardware qubits. In addition, we compare the dynamics of the output probabilities on the processor IBM Q Yorktown within one and a half years of our use of this processor. They clearly demonstrate the significant progress made in the hardware of quantum computers. © 2020, Springer Nature Switzerland AG.