  We present a unified approach to the problem of degeneracy lifting in
geometrically frustrated magnets with and without an external field. The method
treats fluctuations around a classical spin configuration in terms of a
real-space perturbation expansion. We calculate two lowest-order contributions
for the Heisenberg spin Hamiltonian and use them to study the magnetization
processes of spin-$S$ triangular and kagom\'e antiferromagnets.
