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I am limiting myself to fields defined in the three dimensional Euclidean Point Space. The curl of a tensor can be found in these simple steps:

1. Take the simple composition of the second-order tensor, T, with the LeviCivitaTensor[3]. This is effected by the command, Dot [T,LeviCivitaTensor[3]]
2. Take the transpose of the divergence of the above result using the command: Transpose[Div[Dot[T, LeviCivitaTensor[3]],{x,y,z}]] The result you get here is the second-order tensor that is the curl of the tensor T.