Multiwall carbon nanotubes (MWCNTs) fabricated by chemical vapor deposition contain magnetic nanoparticles. While increasing frequency of electromagnetic field (EMF) exposure (up to <10 kHz) of MWCNTs resulted in slight induced magnetization decrease due to skin effect of the conducting carbon, we discovered that higher frequencies (>10 kHz) contained an exponential magnetization increase. We show that puzzling magnetization increase with decreasing magnetic field amplitude (less than 0.5 A/m for 512 kHz) is due to matching the field amplitudes of the magnetic nanoparticles inside nanotubes. This observation reveals a possibility of magnetic tunneling in MWCNTs (change of magnetic state of blocked magnetic moments). This interpretation is supported by observation of unblocking larger magnetic remanence (MR) portion from MWCNTs with progressively smaller amplitude of oscillating magnetic field.