Graphite ion chambers and semiconductor diode detectors have been used to make measurements in phantoms but these active devices represent a clear disadvantage when considered for in vivo dosimetry. In such circumstance, dosimeters with atomic number similar to human tissue are needed. Carbon nanotubes have properties that potentially meet the demand, requiring low voltage in active devices and an atomic number similar to adipose tissue. In this study, single-wall carbon nanotubes (SWCNTs) buckypaper has been used to measure the beta particle dose deposited from a strontium-90 source, the medium displaying thermoluminescence at potentially useful sensitivity. As an example, the samples show a clear response for a dose of 2Gy. This finding suggests that carbon nanotubes can be used as a passive dosimeter specifically for the high levels of radiation exposures used in radiation therapy. Furthermore, the finding points towards further potential applications such as for space radiation measurements, not least because the medium satisfies a demand for light but strong materials of minimal capacitance.