In magnets with strong quantum fluctuations, paramagnetic ground states with or without confinement of spinon excitations can be realized. Here we discuss the physics of the confined phase in the vicinity of a confinement-deconfinement transition: this regime, likely relevant to a multitude of frustrated spin systems, is characterized by multiple length scales. In addition to the magnetic correlation length, a confinement length can be defined, which can be probed, e.g., by local static measurements near nonmagnetic impurities. We illustrate the ideas by explicit calculations for dimerized spin chains, but our qualitative results remain valid in higher dimensions as well. In particular, we study crossover from weak to strong confinement visible in the antiferromagnetic polarization cloud around a nonmagnetic impurity. We also discuss the effective magnetic interaction between impurities, relevant for impurity-induced magnetic order, and consequences for nuclear magnetic resonance and neutron-scattering experiments.