One way to find a calf is with a stock dog. The cows know me and are not worried about their calves if I go around on foot so if they have their calf hidden they won't give away where they are.
But if you dont mind giving the old girls a worry, and you have a well trained stock dog who really will go where you send it, the cows worry too much to keep the calf hidden with the dog around and will run off to the calf to defend it.
I will take the dog with me and watch where I think the cow is looking. I send the dog in that direction. Seeing the dog running around gets them worried and they will start looking for that calf in earnest and usually give away the calfs position. At this point you better have a dog you can call off in an instant and send somewhere else other than to you.
I would not take an average mut as that is likely to end in a big wreck - particularly if the dog is clueless and just blunders about, the cow would probably chase the dog. You dont want the dog to come running behind you with a mad cow after it, then you are in trouble.
Done with tact with a wide casting obedient dog there is not much stress or problem. Just seeing the dog from a fair distance is often enough for them to go and get their baby.
I have also found through much experience that if a dog is on a Quad bike the cows anti-dog instinct, even with calving ones, does not seem to switch on. If that dog jumps onto the ground around calving cows all be nice can break loose. Pretty much goes for sheep as well. It depends on the dog too - some dogs are hated by calving cows and others dont worry them so much. A professional stock dog trainer reckons it is the intent of the dog the cows are reading and I think he is right.