[en] The ground state properties of S=1/2 anisotropic Heisenberg magnets with plaquette frustration are investigated. The models can be classified according to whether a straightforward generalization of the Marshall (1955) Ansatz can be applied, or the ground state has to be approximated by a linear combination of Ising ground states. In the former case, the quantum ground state may have a zero point entropy. In the latter case, a unique ground state with quantum-liquid-like coherence properties is postulated, generalizing an earlier suggestion by Fazekas and Anderson (1974). (author)