The Mu2e calorimeter is composed of two disks each containing 1348 pure CsI crystals, each crystal read out by two arrays of 6x6 mm2 monolithic SiPMs. The experimental requirements have been translated in a series of technical specifications for both crystals and SiPMs. Quality assurance tests, on first crystal and then SiPM production batches, confirm the performances of preproduction samples previously assembled in a calorimeter prototype and tested with an electron beam. The production yield is sufficient to allow the construction of a calorimeter of the required quality in the expected times.