Welcome! I am Dr. Altman, a licensed veterinarian and happy to answer your questions today.
I apologize no one has assisted you yet today and Squangus is not feeling well
It sounds like this is more respiratory like he is coughing with a terminal retch versus attempting to vomit. Is that accurate? If he is acting normal otherwise then it would be fine to monitor him with frequent trips into the bathroom for the steam of the shower to soothe his lungs and trachea
But if he is lethargic, has a reduced appetite, resting respiratory rate (breaths he takes in one minute while resting) is consistently >60, gums are pale, blue, purple and dry to the touch then it would be best to have your vet evaluate him to rule out heart or lung issues with his age.
It could be simple kennel cough
but in a senior pet that is continuing to cough and has any of the above signs he will at the least need to be on antibiotics to treat the cough with it not subsiding, especially being a weekend is upon us and I would hate for you to be at the veterinary er this weekend...
I hope this information makes sense but please let me know how else I can assist you both today. I hope he is feeling better soon!
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