Use ～ところを when you break into, or acknowledge breaking into, a situation already under way — most often as a polite preface in business (お忙しいところを…, ご多忙のところを…). It also appears in reporting to mark a course of events that would have unfolded a certain way but was diverted (本来なら〜ところを). The を marks the interrupted situation as the object of the intruding action, so a transitive verb of disturbance (お邪魔する, 失礼する, 恐縮する, 引き止める) or a reversal typically follows.