～ところを ～even though (at this time, in this state)

「～時・状況なのに・～だったのに」
Shows consideration for other partys situation and that speaker has done something regardless of that situation. Often used ideomatically in greetings to show gratitude. Also seen in phrases such as お休みのところを、ご多忙のところを

（１）その試合は、もう少しで終わるところを、雨で中断された。
Just at the moment the match was about to finish, it was cancelled becuase of rain.

（２）黙っていてもいいところを彼は「私がやりました」と自分から正直に言った。
Just at the moment it was best to have stayed quiet, he himself honestly said "It was me that did it!"