To evaluate the effect of undersaturation of magnetic hysteresis loops measured in moderate (<2 T) fields in magnetically hard minerals such as goethite or hematite, we measured room temperature hysteresis loops in a 7 T field and DC backfield demagnetization curves in fields up to 3 T using an MPMS 3 instrument. Sediments from different regions of the East European platform, mostly of Carboniferous age were used for this study. Similar experiments were also carried out for a small collection of archaeological ceramics (bricks) apparently containing a High Coercivity Low unblocking Temperature (HCLT) magnetic phase (ε-Fe₂O₃?). Hysteresis measurements were complemented by thermomagnetic analysis at low and high temperatures, microscopic observations, and X-ray diffraction studies. High-field magnetic hysteresis loops alone appear insufficient to definitively discriminate goethite from hematite, though there is, expectedly, a tendency that increasing goethite content leads to magnetic hardening, with coercive force reaching 1 T and coercivity of remanence 1.7 T. At the same time, ε-Fe₂O₃ can seemingly be distinguished from either hematite or goethite due to its high saturation magnetization. However, combining hysteresis measurements with low- and high-temperature thermomagnetic analysis provides a much better insight into the magnetic mineralogy of samples. Still, acquiring the reference data on well characterized hematite, goethite, and ε-Fe₂O₃ samples is highly desirable.