
feeling (much) obliged; being (very) grateful; being thankful
feeling sorry (for troubling someone); feeling ashamed (e.g. of an error); feeling embarrassed (e.g. by someone's compliments, hospitality, etc.)
このようなお礼を頂いて恐縮です。
I'm humbled to receive such a gift.
恐縮ですが、少々お待ちください。
I'm sorry, but please wait a moment.
お忙しいところ恐縮ですがご確認をお願いいたします。
I'm sorry to bother you when you're busy, but please check this.