The effect of confinement on the coalescence of Newtonian (polydimethylsiloxane) droplets in a Newtonian (polyisobutylene) matrix is investigated experimentally. A counter rotating parallel plate device, equipped with a microscopy setup, is used to visualize two interacting droplets during shear flow. The ratio of droplet-to-matrix viscosity is kept constant at 1.1. Droplet collisions are studied for a range of droplet sizes, both in bulk conditions and for gap spacings that are comparable to the droplet size. As a result, we present the first quantitative experimental data set for the coalescence of two equal-sized droplets in a pure shear flow with varying degrees of confinement. Compared to bulk conditions, for droplets smaller than roughly 0.2 times the gap spacing, a slight degree of confinement only decreases the orientation angle at which the droplets coalesce whereas the critical conditions for coalescence remain unaltered. For more confined conditions, the critical capillary number up to which coalescence can occur, increases. Therefore, confinement clearly promotes coalescence. In addition, the droplet trajectories, the time-dependent orientation angle of the droplet pair, and the droplet deformation prior to the coalescence event are systematically studied, and a comparison between the confined and the unconfined situation is provided. It is shown that the presence of two parallel walls can induce changes in the flow field around the droplet pair, which cause an increase of the interaction time between the droplets. Moreover, for sufficiently confined droplets, the additional force originating from the presence of the walls becomes comparable to the hydrodynamic force on the droplet pair, thus influencing the drainage of the matrix film between the droplet surfaces.