The tremors - measuring 0.8 and 1.7 on the Richter scale - occurred within 10 minutes of one another at about 21:50 on Wednesday.
Maps showed the location as about midway between Maryport in Cumbria and Kippford in Dumfries and Galloway.
The larger quake showed up on monitoring stations on the mainland.
Two minor earthquakes have been recorded in the middle of the Solway Firth between Dumfries and Galloway and Cumbria.