Materials characterisation by non-invasive analytical methods is already a standardised practice in Archaeology. However, problems may arise in the chemical identification of certain materials that lead to erroneous interpretations. In this study, we address the case of a fragment found in the well-documented archaeological site of Colonia Celsa (Velilla de Ebro, Zaragoza, Spain), first labeled during fieldworks as a glass fragment, subsequently this hypothesis was descarted by macroscopic archaeological recognition, then it was analyzed and identified as a natural resin, and finally, as a polymer blend upon a reinterpretation of the chemical characterisation. Based on this case of study, a methodological protocol for characterising unknown materials using non-invasive analytical methods was developed. A set of reference samples from natural resins were analysed using a portable X-ray fluorescence spectroscopy, Raman spectroscopy, Fourier-transform infrared spectroscopy, and finally, gas chromatography-mass spectrometry as a reference method. The obtained data were statistically processed to assess affinities and differences between the analysed samples, and the results of the different techniques were compared, indicating that the sample was a blend of high-density polyethene with ethylene vinyl acetate, (i.e., an out-of-place artefact). The reported procedure may be useful for specialists working in archaeological science and a warning signal in archaeometry studies.