You generally do not need to present a paper certificate. State licensing agencies can verify electronically reported training completion in the FMCSA Training Provider Registry (TPR).
For Hazardous Materials applicants, the required ELDT theory completion must be on record before the state-administered knowledge test. For Class A, Class B, Passenger, and School Bus applicants, the applicable theory and behind-the-wheel training must be completed before the state-administered skills test.
Your state may have additional requirements, so confirm what to bring with your State Driver Licensing Agency or testing location.