Anticipatory breach of a fundamental term of a contract provides the other party the immediate right to forego any futher obligations on their part, and also an immediate cause of action (Central Trust Co. v. Chicago Auditorium Ass'n, 240 U.S. 581 (1916)).
The equitable remedies of specific performance or injunction would generally be available to prospectively protect confidential information (Rugen v. Interactive Business Systems Inc., 864 S.W.2d 548 (Tex. App. 1993)).
For additional certainty, many non-disclosure agreements specifically say that injunctive relief is available as a remedy. It may be worded something like (borrowed from a sample from the Association of Corporate Counsel):
party A is entitled to obtain injunctive relief against the threatened breach of this Agreement or the continuation of any such breach by party B, without the necessity of proving actual damages...