An air ambulance from Aberdeen was also trying to land.
A spokeswoman for Loganair has since revealed that the problems were due to weather conditions in the area.
The conditions means that those flights that were meant to land in Sumburgh during this period were either cancelled or diverted back to their original departure locations.
The spokeswoman said: “Weather conditions at Sumburgh Airport today unfortunately meant that a small number of our aircraft were unable to land and were either diverted back to the original departure locations or cancelled.”
The airline apologised for any inconvenience caused by the diversions and cancellations: “We apologise for any disruption caused and are working with our customers to move them on to new flights.
“The safety of our crew and passengers remains our number one priority.”
Planes seen circling Sumburgh airport unable to land