Are dogs and cats able to shed tears?

Yes, they do have tear ducts...I think.

They are physically able to shed tears, but the correlation between tears and sorrow is up for debate. We know our companion animals have feelings. But can we push our pets to teary meltdowns? Some vets have reported seeing this phenomenon. Others say they have needed tissues to wipe away animal tears.

Neither one of these animals have tear ducts, so no, they cannot shed tears.