The subjects of this research are the burial clothes of Polish King Sigismund III Vasa and his wife Constance, which were woven and embroidered with silk and metal threads. Fragments of the textiles underwent spectroscopic, spectrometric, and thermogravimetric analyses. The hydrofluoric acid extraction method was improved to isolate various classes of dyes from the textile samples that had direct contact with human remains. High-performance liquid chromatography, coupled with diode array and tandem mass spectrometry detectors with electrospray ionization (HPLC-DAD-ESI-MS/MS) facilitated the detection and identification of colorants present in the textiles. Cochineal, indigo-, madder-, orchil-, and tannin-producing plants were identified as the sources of dyes used. Scanning electron microscopy with an energy-dispersive X-ray detector (SEM-EDS) was employed to identify and characterize the silk fibers and mordants and the metal threads. The presence of iron, aluminum, sodium, and calcium in the silk threads suggests their potential use as mordants. The analysis of the metal threads revealed that most of them were made from flattened gilded silver wire, with only a few being cut from a sheet of metal. Typical degradation mechanisms of metal threads were shown, resulting from both burial environment and earlier manufacturing process, and the use of the textiles in clothing, i.e., a significant loss of the gold layer was observed in most of silver gilt threads, caused by abrasion and delamination. The results of the thermal analysis confirmed the presence of silk and silver threads in the examined textiles.