Untethering can allow soft modular robots to move from the laboratory test bench into realistic environments and commercial use. However, today’s state of the art soft modular robots remain electrically connected to external power sources and controllers. The reason for this is that current electrical connections between modules induce rigidity into the soft robot, eliminating the advantages of being soft or can have high electrical resistance making communication and power exchange among modules impractical. To overcome this, we present a new bio-inspired inter-module connection strategy that connects soft modules mechanically and electrically without sacrificing the high deformability of the robot nor the low electrical resistance. We show that our strategy allows connected modules to retain stiffness in the same order of magnitude as individual modules while providing low electrical resistance. This enabled us to develop two untethered soft modular tensegrity robots, a gripper capable of holding two times its body weight and grasp objects of different shapes and a crawler that can move up to 4.5cm/min.