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Crilin (Crystal Calorimeter with Longitudinal Information) is asemi-homogeneous, longitudinally segmented electromagnetic calorimeter based onhigh-$Z$, ultra-fast crystals with UV-extended SiPM readout. The Crilin designhas been proposed as a candidate solution for both a future Muon Colliderbarrel ECAL and for the Small Angle Calorimeter of the HIKE experiment. As apart of the Crilin development program, we have carried out beam tests of small($10\times10\times40$~mm$^3$) lead fluoride (PbF$_2$) and ultra-fast leadtungstate (PbWO$_4$, PWO) crystals with 120~GeV electrons at the CERN SPS tostudy the light yield, timing response, and systematics of light collectionwith a proposed readout scheme. For a single crystal of PbF$_2$, correspondingto a single Crilin cell, a time resolution of better than 25~ps is obtained for$>$3 GeV of deposited energy. For a single cell of \pwo, a time resolution ofbetter than 45~ps is obtained for the same range of deposited energy. Thistiming performance fully satisfies the design requirements for the MuonCollider and HIKE experiments. Further optimizations of the readout scheme andcrystal surface preparation are expected to bring further improvements.

Beam test, simulation, and performance evaluation of PbF$_2$ and PWO-UF  crystals with SiPM readout for a semi-homogeneous calorimeter prototype with  longitudinal segmentation