Professional sound level meters will do peaks. You may not see it on screen because it is not displaying the sound level fast enough, but it will store the peak in memory for subsequent readout.
You can also record "L" values (e.g., "L5") which would be the sound level exceeded X% (e.g., 5%) of the time. These are typically used in regulatory compliance. For example, an ordinance may specify that the sound at the property line is not to exceed a level of 70 dB for 15 minutes per hour (L25), or 65 dB for 30 minutes per hour (L50).
The display shown here is in "Fast Response" with "Linear Weighting."


