Precise timing capability will be a key aspect of particle detectors at future high energy colliders, as the time information can help in the reconstruction of physics events at the high collision rate expected there. Other than being used in detectors for PET, fast scintillating crystals coupled to compact Silicon Photomultipliers (SiPMs) constitute a versatile system that can be exploited to realize an ad-hoc timing device to be hosted in a larger high energy physics detector. In this paper, we present the timing performance of LYSO:Ce and LSO:Ce codoped 0.4% Ca crystals coupled to SiPMs, as measured with 150 GeV muons at the CERN SPS H2 extraction line. Small crystals, with lengths ranging from 5 mm up to 30 mm and transverse size of 2×2mm2 or 3×3mm2, were exposed to a 150 GeV muon beam. SiPMs from two different companies (Hamamatsu and FBK) were used to detect the light produced in the crystals. The best coincidence time resolution value of (14.5±0.5)ps , corresponding to a single-detector time resolution of about 10 ps, is demonstrated for 5 mm long LSO:Ce,Ca crystals coupled to FBK SiPMs, when time walk corrections are applied.