You use coincidentally when you want to draw attention to a coincidence.
例句
Coincidentally, I had once found myself in a similar situation...巧得很，我曾经碰到过类似的情况。They immediately got in touch with Dr Ting who was, purely coincidentally, also in California...他们立即与丁博士联系，真是巧得很，他也在加利福尼亚。