offer (someone) (one's) condolences
To extend a semi-formal declaration or expression of sympathy to someone who has experienced a recent pain, grief, or misfortune, especially the death of a relative or loved one. Tom, I just heard about your wife's passing and wanted to offer my most sincere condolences. We're calling over after lunch to offer condolences to the family. Jane wasn't able to make it to the funeral, but she wanted to offer you her condolences nonetheless.