There is one confirmed amphitheatre in Scotland and two possible. Many Roman forts had an oval enclosed area for entertainment, exercising horses and combat. These were normally built of wood so not many can be found today. An amphitheatre was usually a short distance away from a fort and would use the contours of the land to create a seated terraced effect.

Melrose/Newstead (Trimontium Amphitheatre)

Source: Trimontium Amphitheatre, Newstead, Scottish Borders. – Trimontium Museum
Musselburgh Amphitheatre

In 1995 a circular structure was found next to Lewisvale public park and academics think it may be the post holes for a wooden amphitheatre. The Roman fort in Musselburgh is nearby.
Source: A Semi-Elliptical, Timber-Framed Structure at Inveresk (The Most Northerly Amphitheatre in the Empire?) on JSTOR (login required)
Falkirk Amphitheatre
The Falkirk History Society has been looking for the location of the amphitheatre near Camelon Fort and they think they have found it near Camelon railway station.

Source: An Amphitheatre in Camelon?