A Coastguard spokeswoman said they were hoping to get in contact with the parents of the two boys.
She said: "We would like to hear from the parents to confirm that the children are, in fact, safe."
It is understood that the boys were reported missing at midday but the parents had not been in contact with the emergency services since about 1pm.
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The Labour leader said newspapers were going "a little bit James Bond" over the "increasingly wild and entirely false" claims.
The "astonishing" find was made during an excavation at Vindolanda, near Hexham in Northumberland.