To have tears in one's eyes; to be moved to the point of tears (often a slight or restrained form of crying).
彼女は映画の最後の場面で涙ぐんでいた。
She had tears in her eyes during the final scene of the movie.
おじいさんの話を聞いて、子どもが目を涙ぐませた。
Hearing his grandfather's story, the child got teary-eyed.
卒業式で友達と別れるとき、彼はこらえきれずに涙ぐんだ。
At the graduation ceremony when saying goodbye to friends, he couldn't hold back and became teary-eyed.