Determining the orbital periods of cataclysmic variable stars (CVs) is essential for confirming candidates and for the understanding of their evolutionary state. The Transiting Exoplanet Survey Satellite (TESS) provides month-long photometric data across nearly the entire sky that can be used to search for periodic variability in such systems. This study aims to identify and confirm the orbital periods for members of a recent compilation of magnetic CVs (known as polars) using TESS light curves. In addition to providing the periods, we set out to investigate their reliability, and hence the relevance of TESS for variability studies of CVs. Four period-search methods were used, namely the Lomb-Scargle periodogram, the autocorrelation function (ACF), sine fitting, and Fourier power spectrum analysis, to detect periodic signals in TESS light curves. We investigated the correlation between noise level and TESS magnitude by "flattening" the observed TESS light curves, effectively isolating the noise from the periodic modulation. To evaluate the reliability of the period detections, we developed a probabilistic framework for the detection success across signal-to-noise ratios in the power spectral density of observed light curves. Ninety-five of the 217 polars in our sample have pipeline-produced TESS two-minute cadence light curves available. The results from our period search are overall in good agreement with the previously reported values. Out of the 95 analysed systems, 85 exhibit periods consistent with the literature values. Among the remaining ten objects, four are asynchronous polars, where TESS light curves resolve the orbital period, the white dwarf's spin period, and additional beat frequencies. For four systems, the periods detected from the TESS data differ from those previously reported. For two systems, a period detection was not possible due to the high noise levels in their light curves. Our analysis of the flattened TESS light curves reveals a positive correlation between noise levels - expressed as the standard deviation of the flattened light curve - and TESS magnitude. Our noise level estimates resemble the rmsCDPP, a measure of white noise provided with the TESS pipeline products. However, our values for the noise level are systematically higher than the rmsCDPP indicating red noise and high-frequency signals hidden in the flattened light curves. Additionally, we present a statistical methodology to assess the reliability of period detections in TESS light curves. We find that for TESS magnitudes >~17, period detections become increasingly unreliable. Our study shows that TESS data can be used to reliably and efficiently determine orbital periods in CVs. The developed methodology for period detection, noise characterisation, and reliability assessment can be systematically applied to other variable star studies, thus improving the robustness of period measurements in large photometric data sets.

Cone search capability for table J/A+A/703/A166/tablea1 (properties and period search results for 95 polars with TESS 2-minute cadence light)