Do sheep have a cardiac sphincter?

Yes, they would have to, otherwise the digesta from the rumen and reticulum would be free come up if the stomach compartments get quite full. It is found at the junction between the esophagus and the ruminal/reticular junction. When a bolus of cud is to be regurgitated, the sphincter muscle relaxes and allows the cud to come up to be chewed, and relaxes again to allow the rechewed bolus to be returned to the rumen. Cardiac sphincters are also found between most of the chambers in the ruminant animal for the same reason as stated above. Check out the three sources below for further information and pictures for proof: