Anhydrite is considered a rare mineral phase in magmas, with only ∼33 documented occurrences worldwide. However, anhydrite readily decomposes in the near-surface environment, making it difficult to recognize its former presence in rocks collected at or near Earth’s surface. In such samples, only small anhydrite inclusions fully shielded within other minerals can have survived. During a recent field trip to the southwestern USA, we sampled 17 Laramide-age (ca. 40−80 Ma) magma systems, most of which are associated with porphyry copper deposits. A systematic search for anhydrite inclusions preserved within apatite, amphibole, plagioclase, and quartz phenocrysts in ∼100 rock samples by optical microscopy and Raman spectroscopy revealed that each of these 17 magma systems was at least temporarily anhydrite-saturated. Also, most previously identified magmatic anhydrite-bearing intrusions are associated with porphyry copper deposits, and both intrusive and volcanic rocks containing magmatic anhydrite show high Sr/Y ratios. These observations suggest that anhydrite saturation and porphyry copper formation are linked via magma fractionation at high pressure. Compared to average arc magmas, anhydrite-bearing magmas are unusually oxidized and sulfur-rich and seem to also be unusually water-rich. Hence, our preferred interpretation is that magma generation and/or fractionation at high pressure promotes the formation of superhydrous and oxidized magmas, which in turn promotes high sulfur contents and ultimately the precipitation of anhydrite. The high mineralization potential of these magmas does not need to result from their high sulfur content but could be caused by other properties of high-pressure magmas.