21st Century Energy Workforce Act This bill directs the Department of Energy (DOE) to establish a National Center of Excellence for the 21st Century Workforce Advisory Board to (1) support and develop training and science education programs, (2) align apprenticeship programs and industry certifications to further develop succession planning in the energy sector, (3) integrate educational standards to develop foundational skills for elementary and secondary education and postsecondary education to create a pipeline between education and career, and (4) support the replication of existing model energy curricula. DOE shall also establish a pilot program to award grants on a competitive basis to eligible entities for job training to obtain an industry-recognized credential. Grant amounts are limited to $1 million for any one year. The federal share of the cost of a job training and education program using a grant shall be up to 65%, while the non-federal share may not be less than 50% cash.