How to notify check when a player leaves himself in check I'm learning to play chess. 

Twice we had a situation where the white player moved a piece that was blocking the black Queen from checking the white King. There was no move available to announce "Check".

What is the proper procedure here?
It's not technically a check since Black wasn't making a move to check White's king. White made an illegal move that placed his King under attack.

Black should mention that White made an illegal move, getting White to take the move back and play something else. If you're playing in a tournament, you could call the arbiter over and say White made an illegal move (often 3 illegal moves = forfeit).