In the design of long, flexible medical devices that are inserted into a lumen by pushing them from their proximal end (e.g., catheters, scopes, cochlear-implant electrode arrays), there is a fundamental trade-off between making the device flexible/soft to safely conform to the environment, and making the device stiff to enable the device to be inserted without buckling. A number of continuum medical devices have incorporated magnetic actuation, typically at the distal end to magnetically steer the device in a desired direction. This type of magnetic actuation can reduce insertion forces and/or delay buckling by reducing the total friction between the continuum device and the environment. However, because the magnetic actuation is limited to the distal end, its effectiveness is reduced with increased insertion depth. Our group recently proposed a magnetic-actuation concept for soft, untethered endoluminal robots in which the soft robot has two or more axially magnetized permanent magnets distributed along its length, with the magnetization direction alternating between neighboring magnets, and a rotating external magnet is used to induce a traveling wave in the soft device, causing it to crawl in a deterministic and reversible direction. In this paper, we extend this concept to soft continuum devices that are inserted by pushing them from their proximal end. Our basic hypothesis is that if the magnetic-actuation concept is sufficient to cause crawling in untethered devices, it will also reduce the insertion forces required to insert continuum devices. We show that this is, in fact, the case. We also show that, in limiting cases, it is even possible to reduce the insertion forces to zero such that the continuum device inserts itself without any proximal-end push.