Two other men were also spotted on the track taking photographs.
The viaduct is on the route of the Jacobite Steam Train and is seen in the Daniel Radcliffe films when the Hogwarts Express crosses over it.
British Transport Police (BTP) said it has recently been made aware of a number of incidents where people have been trying to view or photograph trains as they pass over the iconic structure.
BTP constable Nicky Ritchie said: "We know that visitors, many of them foreign, want to enjoy this incredibly scenic area and are keen to see and capture the trains, particularly steam trains, crossing what is without doubt a magnificent structure.
"However, they have to realise that they need to do it safely and without breaking the law."
Mark Henderson, senior community engagement manager for Network Rail, warned of the dangers of trespassing.
He said: "Trains travelling at speed take a long time to stop and anyone struck by one is likely to be killed or very badly injured.
"We work closely with BTP to educate the public on the dangers of misusing the railway and are committed to making sure people fully understand the risk they face when straying onto operational railway land."
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