Analytical models for the design and evaluation of checkpointing of real-time tasks are developed. First, the execution of a real-time task is modeled under a common assumption of perfect coverage of on-line detection mechanisms (which is termed a basic model). Then, the model is generalized (to an extended model) to include more realistic cases, i.e., imperfect coverages of on-line detection mechanisms and acceptance tests. Finally, we determine an optimal placement of checkpoints to minimize the mean task execution time while the probability of an unreliable result (or lack of confidence) is kept below a specified level. In the basic model, it is shown that equidistant intercheckpoint intervals are optimal, whereas this is not necessarily true in the extended model. An algorithm for calculating the optimal number of checkpoints and intercheckpoint intervals is presented with some numerical examples for the extended model.