Usually, a litigants own lost time will not be a compensable item of damages in legal systems derived from those of England called "common law" jurisdictions (including England, Ireland, the United States, Canada, New Zealand and Australia), unless there is an contractual provision that provides that "time is of the essence" and some liquidated damages clause in the contract that quantifies this harm.
Usually, a litigants own lost time will not be compensable in a tort action.
But, while lost time is not compensable as a general rule, lost income (either from wages or profits) usually is compensable so long as it is foreseeably caused by the breach of a legal obligation, and is not merely speculative.
When money or property is withheld for some time period, there will also often be an element of pre-judgment interest that is calculated on top of the economic value of the harm as of the time of the breach, often at a statutory rate, although the law of pre-judgment interest varies quite a bit from jurisdiction to jurisdiction and is often allowed in contract lawsuits, but not in tort lawsuits.
Outside of these jurisdictions, there is further variation. One of the few instances in which lost personal time in breach of a promise is compensable of which I am aware is on a Japanese passenger rail line (including the equivalent of subways). There, passengers are entitled to a fixed amount of compensation automatically when the train fails to arrive on time (without regard to the individualized value of a person's time).