Accelerator mass spectrometry (AMS) is a worldwide recognized method for radiocarbon (14C) dating. The advantageous aspects of this method include the variety of materials and the small sample size (1 mg of carbon) that can be measured. However, these pose several challenges in the laboratory, such as developing appropriate chemical pretreatment methods. In the summer of 2022, the Radiocarbon and Mass Spectrometry Laboratory in Gliwice, Poland, launched the MICADAS accelerator spectrometer. The report on background and reference materials measurement results for the period from September 2022 to July 2024 is presented in this publication. Quality assurance and quality control processes are extremely important to guarantee the high quality of the results obtained in the laboratory. Hence, our Radiocarbon and Mass Spectrometry Laboratory in Gliwice took part in the Glasgow International Radiocarbon Inter-Comparison (GIRI) program. The radiocarbon ages for wood, bone, humic acid, and barley mash samples were determined and compared with reported values. The resulting data confirmed that our Laboratory is capable of dating samples across a spectrum of materials and ages ranging from contemporary to the limits of the radiocarbon method, achieving precision on par with that of other laboratories.