A combined system for solidification and instability detection during the forced extrusion of polymers is constructed and first investigations are presented. The system comprises a home built Halbach‐type NMR magnet, monitoring the NMR relaxation at different positions along the extrudate length, and a highly sensitive transducer in the die recording mechanical pressure fluctuations. The system is complemented by an optical extrudate visualization setup. First results are shown for low density and high density polyethylene (LDPE and HDPE), which have different branching structures. Three relevant processing parameters were varied during the investigations, i.e., extruder rotation speed, draw ratio and extrusion temperature. Overall, the characteristics of NMR relaxation show a clear dependence on the magnet position along the extrudate length, which can be related to the cooling, onset and propagation of crystallization, and solidification of the polymer melt. The coupling of a low‐field NMR with a high sensitivity instability detection system shows the potential of creating a versatile tool for a unique online control method in polymer processing. In the future, this combination could provide insight into the influence of branching structures on polymer processing of polyethylene, for example.