An approach is presented for calculating the binding energy of neutral donors in semiconductor heterostructures. The technique avoids the need for analytical solutions. A generalization of the method to include central cell corrections, effective mass, and dielectric mismatch at heterojunctions, together with band nonparabolicity, is discussed. The utility of the method is demonstrated via a study of the spin-flip Raman spectrum of double quantum wells. Finally it is shown how spin-flip Raman spectroscopy could be used, in conjunction with doping of donors, as a probe of the possible enhancements to the paramagnetism of a dilute magnetic semiconductor at a heterojunction with a nonmagnetic material.