There are two main equitable remedies for breach of contract.
Specific performance - this is an order directing the breaching party to perform the contract in the way specified by the court. It will only be ordered if damages will not provide adequate compensation and will not be awarded in relation to contracts of personal service.
Injunctions - these are orders directing a party not to do something - eg, not to persist with a contractual breach.
Both remedies are discretionary; the court is not obliged to award them even where breach is established.
Equitable damages may also be available in some cases
Detailed discussion forthcoming