。
She thought her watch was the same one as mine.
Literal
She [topic-は] her own watch [object-を] my watch [with-と] same thing-だ [quotative-と] thought.
自分の時計を marks the watch as the matrix object; the quoted clause 私の時計と同じものだ describes what she thought of it. ~と同じ ('the same as X') marks the standard of comparison with と. もの ('thing') here serves to package 'same' as a noun ('the same thing'), so the copula だ can attach. The quotative と + 思った wraps the whole judgment as the content of her thought.