Archeological finds are usually just the missiles that were used .
Caerphilly Castle in Wales has several on display , plus it has 4 reconstructions (authentic as far as they have been able to ascertain) of medieval siege engines . If you are lucky you can visit on a day when they demonstrate these , if not then there is a video of each of them being fired into the moat/lake .
I think the last recorded use of a trebuchet was by the Turks(or whatever they were called at the time) against British ships in the Bosphorous . But that was not medieval and it wasn't a siege .