Programmable shape morphing enables soft machines to safely and effectively interact with the environment. Stimuli-responsive materials can transform 2D sheets into 3D geometries. However, most solutions cannot hold their shape at zero power, are limited to predetermined configurations, or lack sufficient mechanical stiffness to manipulate common objects. We demonstrate here segmented soft electromagnetic actuators integrated with shape memory polymer (SMP) films, capable of deforming and latching into a broad range of configurations. The device consists of liquid metal (LM) coils in an elastomer shell, laminated between two SMP films. The coils are linked by narrow joints, on which stretchable heaters are patterned. Heating the SMP greatly reduces its stiffness. Driving current through an LM coil in the presence of a magnetic field then leads to large bending or twisting. Cooling the SMP locks in the shape, leading to load-bearing capacity. Complex shapes are obtained from an initially flat device.