look for (someone or something) high and low
To look absolutely everywhere for someone or something; to search exhaustively for someone or something. We've been looking for an apartment we can afford high and low, but the housing market in this town is atrocious. We were looking for you high and low—thank goodness you're all right!
look for someone or something high and low
and look high and low (for someone or something)to search everywhere for someone or something. Where were you? I looked for you high and low. I looked high and low for my passport.