Carbon nanotubes (CNTs) can be spun into fibers as potential lightweight replacements for copper in electrical current transmission since lightweight CNT fibers weigh <1/6th that of an equivalently dimensioned copper wire. Experimentally, it has been shown that the electrical resistance of CNT fibers increases with longitudinal strain; however, although fibers may be under radial strain when they are compressed during crimping at contacts for use in electrical current transport, there has been no study of this relationship. Herein, we apply radial stress at the contact to a CNT fiber on both the nano- and macro-scale and measure the changes in fiber and contact resistance. We observed an increase in resistance with increasing pressure on the nanoscale as well as initially on the macro scale, which we attribute to the decreasing of axial CNT…CNT contacts. On the macro scale, the resistance then decreases with increased pressure, which we attribute to improved radial contact due to the closing of voids within the fiber bundle. X-ray photoelectron spectroscopy (XPS) and UV photoelectron spectroscopy (UPS) show that applied pressure on the fiber can damage the π–π bonding, which could also contribute to the increased resistance. As such, care must be taken when applying radial strain on CNT fibers in applications, including crimping for electrical contacts, lest they operate in an unfavorable regime with worse electrical performance.