A polite phrase used before asking something or making a request, meaning 'excuse me, but...' often used to soften the following statement.
失礼ですが、お名前をもう一度教えていただけますか？
Excuse me, but could you tell me your name once more?
失礼ですが、こちらの席は空いていますか？
Excuse me, but is this seat free?
失礼ですが、その書類にサインをいただけますか？
Excuse me, but could you sign this document?
A prefatory expression used when stating a frank opinion or criticism politely; similar in use to 'with all due respect.'
失礼ですが、その案は現実的ではないと思います。
With all due respect, I don't think that proposal is realistic.
失礼ですが、もう少し詳しく説明していただけますか？
With respect, could you explain that in a bit more detail?