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A crude method is using traceroute, watching for unexpected latency jumps between hops. If you control devices along the path, and enable SLA responders, your timing information would be much more accurate. (Also, do I recall some Cisco IP SLA has something like traceroute?)
A common cause of latency spikes is queuing congestion. Remediation can be difficult and expensive although if not all traffic needs same service level performance, using QoS might be sufficient for the critical traffic.