The EFQM recognition system is an acknowledged method of assessing business excellence understood as the degree of implementation of quality management in an organization. The paper aims to examine whether a high rating under the EFQM recognition system simultaneously means a high general management maturity level. The investigation covers the 35 organizations that won EFQM awards in Portugal. The study is based on points awarded to organizations under the EFQM recognition system and on questionnaires/interviews with managers responsible for quality management in the studied organizations. The results indicate a positive and robust correlation between the quality management implementation (rating under the EFQM recognition system) and general management maturity. The study helps to close the gap in the literature regarding the relationship between quality management and management maturity in an organization.