Conformance checking is a well-known technique for evaluating the difference between the modeled behavior and the recorded behavior of a process. Currently, most conformance-checking techniques only use the order of executed tasks to evaluate such differences. This approach has a drawback: it cannot correctly evaluate fitness for process executions that violate, for example, the task completion times required by the model. In this paper, we consider process models with time constraints given as timed automata and propose a method for evaluating the fitness of timed traces with timed automaton process models. Our proposed conformance checking evaluates time fitness, a novel concept, as well as the standard fitness of activity orders. For the computation of our proposed fitness, we implement three algorithms: 1) a naïve exhaustive search, 2) an A* algorithm based on alignment, and 3) an improved version of the A* algorithm using time attributes. We conduct several experiments using these algorithms and demonstrate that our proposed method finds the closest model execution path to a trace, which becomes possible by considering time fitness. We also show that our improved A* algorithm outperforms the other algorithms and indicates further areas for improvement.