A magnetically clamped wellbore instrument module includes a substantially non-magnetic housing configured to traverse an interior of the wellbore. At least one electromagnet is disposed at a longitudinally spaced apart position along the housing. The at least one electromagnet has a plurality of circumferentially spaced apart contact points that define a diameter greater than a diameter of the housing. The contact points have circumferential spaces therebetween defining a diameter smaller than the diameter defined by the contact points.