"Engagement" in the sense of promise of marriage would be "yak-hon," but if you are attaching other sentiments, the correct word would be "un-yak," which means promise.

I agree with "yakhon", meaning engagement, but the general practice in KOrea is to inscribe the semi-official term "yakhon kinyum", which stands for "in memory of engagement". Although "unyak" is a good suggestion, I rather think that it is too a general word meaning every kind of promise.
On the other hand, if you wish, you can use "saranghae", which just means "I love you", or "yongwonhee", meaning "forever". You can have millions of expressions that you love her. Once I saw a German guy who presented his German fiance a necklace in the shape of 愛(love). He was a dentist and made that shape by himself using silver. Well, good luck!