  We discuss generalizations of the Szeg\H{o} Limit Theorem to truncated
Toeplitz operators. In particular, we consider compressions of Toeplitz
operators to an increasing sequence of finite dimensional model spaces. We
present two theorems. The first is a new variant of the Szeg\H{o} Limit Theorem
in this setting. The second relates to the variant given by
Strouse-Timotin-Zarrabi in 2017, and characterizes the sequences for which that
result holds.
