At the time the British Museum, amongst others, displayed their collection amongst casts, the Parthenon marbles had casts of the missing parts attached.
The new museum in Athens has something similar with the original marbles displayed with the pieces from other collections present as plaster casts.
Only in the 20th century, with changes of taste were only displays of actual artifacts.
I believe there were models of the Parthenon Colleseum and the Pantheon by Emil Auguste Braun. The model of St Peter's in Rome was donated later.
Oh, and don't forget the model of the Acropolis in Athens, just visible in the centre of this postcard.
One of the images Falkor has posted shows Mr. Cheek, responsible for the repair of the casts in the 20th Century. He would regularly hold repair sessions, which might explain what the Colleseum model was doing in the Renaissance Court.
These casts, some of them huge, were quite mobile though. The Medici casts were evicted from the Italian Court to make way for the "Crystal palace Club", and then in the Roman Court, before appearing in the nave after the First world War.