In times of increasing awareness of limited resources, companies are becoming especially interested in criticality assessments. Based on the existing approaches of ESSENZ (integrated method to assess resource efficiency) and SCARCE (approach is to enhance the assessment of critical resource use at the country level), a method called CS-ESSENZ (company-specific ESSENZ) has been developed to measure the company-specific aspects of criticality and social impact in supply chains for abiotic resources. These comprise 20 categories and corresponding indicators, based on 19 ESSENZ and 25 SCARCE categories. Eleven of these indicators were modified, four were newly developed (e.g., economic importance), and the last five were applied as they are in ESSENZ or SCARCE. CS-ESSENZ was tested using the case study of a smartphone, demonstrating the method’s applicability as well as generating additional information on company-specific improvement potential. The results for supply risk showed that 29 out of 58 ESSENZ hotspots showed high, and 12 showed medium, improvement potential from the company perspective. CS-ESSENZ enables companies to obtain specific information on criticality and social aspects in their supply chains and points out areas for improvement, e.g., with respect to purchasing strategies for cobalt.