The rotating-wave approximation (RWA) is ubiquitous in the analysis of driven and coupled resonators. However, the limitations of the RWA seem to be poorly understood and in some cases the RWA disposes of essential physics. We investigate the RWA in the context of electrical circuits. Using a classical Hamiltonian approach, we find that by balancing electrical and magnetic components of the resonator drive or resonator-resonator coupling, the RWA can be made exact. This type of balance, in which the RWA is exact, has applications in superconducting qubits, where it suppresses nutation normally associated with strong Rabi driving. In the context of dispersive readout, balancing the qubit-resonator coupling changes the qubit leakage induced by the resonator drive but does not remove it in the case of the transmon qubit.