1. The stock market was falling sharply, but Lucy didn’t panic and sell her stocks. Instead she sat tight and waited for the market to rise again.
2. Margie called late at night to tell us that her car had broken down and to ask us to come and pick her up. We told her to sit tight and we would be there as soon as possible.

Synonym: keep (one’s) cool. The expression sit tight is often used in situations of danger or panic or in situations where a calm, cool head is needed. It always uses the adjective “tight” rather than the grammatically correct “tightly”.