Dynamic program monitoring has been applied in software-intensive systems to detect runtime constraint violations and trigger system recovery actions. Uncontrolled monitoring activities may, however, delay detection of a violation for an unbounded time and, worse, affect the original system's schedulability. In this paper, we introduce the concept of predictable monitoring, which demands a bound on detection latency while ensuring temporal non-interference by the monitoring process. We present off-line analysis techniques for predicting the maximum detection latency with fixed-priority scheduling under two types of monitoring schemes: synchronous and asynchronous. For asynchronous monitoring, we illustrate how to achieve predictable monitoring by bounding the detection latency and controlling the monitoring budget using a bandwidth-preserving, server-based approach.