  Crilin (Crystal Calorimeter with Longitudinal Information) is a
semi-homogeneous, longitudinally segmented electromagnetic calorimeter based on
high-$Z$, ultra-fast crystals with UV-extended SiPM readout. The Crilin design
has been proposed as a candidate solution for both a future Muon Collider
barrel ECAL and for the Small Angle Calorimeter of the HIKE experiment. As a
part 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 lead
tungstate (PbWO$_4$, PWO) crystals with 120~GeV electrons at the CERN SPS to
study the light yield, timing response, and systematics of light collection
with a proposed readout scheme. For a single crystal of PbF$_2$, corresponding
to 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 of
better than 45~ps is obtained for the same range of deposited energy. This
timing performance fully satisfies the design requirements for the Muon
Collider and HIKE experiments. Further optimizations of the readout scheme and
crystal surface preparation are expected to bring further improvements.
