The deformation and orientation of droplets during transient shear flow is studied in a counterrotating device using microscopy. The effect of the degree of confinement and viscosity ratio is systematically investigated. The system consists of polydimethylsiloxane droplets of varying sizes and viscosities dispersed in a polyisobutylene matrix. The observations are compared with the predictions of an adapted version of the Maffettone and Minale model [Maffettone, and Minale, J. Non-Newtonian Fluid Mech. 78, 227-241 (1998)] which includes confinement effects [Minale, Rheol. Acta 47, 667-675 (2008)]. For flow start-up at low capillary numbers, the deformation of confined droplets and their orientation towards the flow direction are increased with respect to the unconfined situation for all viscosity ratios under investigation. The confined model results for start-up and the experimental data at low capillary numbers are in good agreement both showing similar monotonous transients. At high degrees of confinement and high shear rates, one or more overshoots in the droplet deformation are experimentally observed, depending on the viscosity ratio. In addition, droplets become sigmoidal when highly confined. Under these conditions, the confined Maffettone and Minale model, which assumes an ellipsoidal droplet shape, cannot be used to predict the droplet behavior. The relaxation of confined droplets upon cessation of steady-state shear flow is also studied. It is experimentally observed that confinement only affects the relaxation at degrees of confinement above 60% of the gap spacing. Highly confined droplets experience a slightly slower relaxation with respect to bulk conditions. The relaxation predictions of the confined model are in rather good agreement with the experimental data.