  A single calorimeter station for the Muon $g-2$ experiment at Fermilab
includes the following subsystems: a 54-element array of PbF$_{2}$ Cherenkov
crystals read out by large-area SiPMs, bias and slow-control electronics, a
suite of 800 MSPS waveform digitizers, a clock and control distribution
network, a gain calibration and monitoring system, and a GPU-based frontend
read out through a MIDAS data acquisition environment. The entire system
performance was evaluated using 2.5 - 5 GeV electrons at the End Station Test
Beam at SLAC. This paper includes a description of the individual subsystems
and the results of measurements of the energy response and resolution,
energy-scale stability, timing resolution, and spatial uniformity. All measured
performances meet or exceed the $g-2$ experimental requirements. Based on the
success of the tests, the complete production of the required 24 calorimeter
stations has been made and installation into the main experiment is complete.
Furthermore, the calorimeter response measurements determined here informed the
design of the reconstruction algorithms that are now employed in the running
$g-2$ experiment.
