Spin-rotation constants and rotational g tensors can be evaluated as second derivatives of the energy with respect to the rotational angular momentum and nuclear spin or angular momentum and external magnetic field, respectively. To overcome problems with the slow basis set convergence and the unphysical (gauge-)origin dependence in quantum chemical calculations of these two properties, we suggest the use of perturbation dependent atomic orbitals (rotational London orbitals), which depend explicitly on the angular momentum and the external magnetic field and are a generalization of the conventional London orbitals (also known as gauge-including atomic orbitals). It is shown that calculations of spin-rotation constants and rotational g tensors based on rotational London orbitals are closely related to London-orbital computations of nuclear shieldings and magnetizabilities. Test calculations at the Hartree-Fock self-consistent-field level for HF, N-2, CO, and CH2O demonstrate the superior convergence to the basis set limit provided by the rotational London orbitals. They suggest that future calculations employing rotational London orbitals in conjunction with highly correlated wave functions will be able to provide results of unprecedented accuracy for spin-rotation constants anti rotational g tensors.