In sailing ships, you don't wind up with triggering queasiness from engine fumes.
If you're on deck and look at the horrizon frequently, you don't get a mismatch of your eyes thinking you're still while your inner ear says you are moving.
Old cookbooks advise heavily gingered foods for sea travelers. Gingerbread, ginger nuts, candied ginger. Ginger settles the stomach.
In Two Years Before the Mast, Richard Henry Dana reports he was horribly seasick after leaving port. One of the old hands told him that, "now that you've gotten that land swash out of your belly," sea rations would put him right. RHD had a big plate of salt meat & onions, and was never seasick again. Okay, it's an anecdote, but it was one of their ways of handling.
Like Zither13's quote about Richard Henry Dana, I found period (my period of study is 17th/early 18th century) quotes suggesting seasickness was primarily a problem for people not used sea travel.
In his Dialogues, Nathaniel Botoler [Butler] when explaining how big a ship is needed for the number of people on board, he notes that extra room is needed for passagers who are apparently more likely to be sea-sick than the sailors:
"But withal there is another inconsiderable practice as full of danger and improvidence as that can be, which is the over pestering of ships with [non-sailor] soldiers and passengers, and especially when they are to pass upon long voyages, into hot countries; for though the allowance of tonnage [referring here to a measure of the size of a ship] for every passenger, with his person and provisions, may be considered, according to the length or shortness of the voyage in hand, ...in voyages of length, especially to the southwards, I shall never advise a less allowance in proportion of room, than of two ton for every man; and especially if they be mere landmen, unused to the sea, who through their seasickness and nastiness procure many infectious diseases as well to themselves as all that sail with them." (Boteler, p. 61)
In Jeremy Roch's Journals, printed in Bruce Ingram's Three Sea Journals of Stuart Times, Captain Roch says of the soldiers being transported in his ship,
"[Oct. 28, 1628] But I was fained to exercise my cudgel [a short stick] very violently ere I could make any of my landsoldiers budge out of the hold, who I verily believe would have rather chosen to lie there and drown than to come up and labour for their lives. Such is the infirmity of sea-sickness and the nature of some men who dare not look upon a danger being threatened them from above, yet make little account of the hazard in entering a breach against men though the mouths of the cannon be against them." (Ingram/Cooper, p. 19)
Still, rough weather apparently made even the most seasoned men ill, as Chaplain Henry Teonge reported in his Diary.
"[Aug. 17-18, 1675) The sea is very turbulent, insomuch that our ship had almost fallen foul on one of our companions, and many of our men are sea-sick." (Teonge, p. 65)
Early in his career, Merchant Captain Nathaniel Uring dealt with the issue, hinting that the quality of food shipboard was a factor.
"Being well recommended to the Master of a Vessel bound thither [Newcastle], I proceeded on the Voyage; but by the Time we were the Length of the Nore, I was extremely Sea-sick, which continued most Part of the Voyage: This, with the bad Provisions aboard, and their ill Manner of dressing them, gave a check to my Fondness of going to Sea, and I heartily repented my choosing that sort of Life; but having enter’d upon it by my own earnest Desire, I resolved with my self, whatever Pain and Hardship I met with, to endure it patiently, and pursue my first Intention. Though I fared very hard during the Voyage, yet I proceeded a Second in the same Vessel; and on my Return to London, I undertook to go to the West Indies in the Swift Galley, Capt. William Read, to whom I was recommended in a particular manner by my Relation, who was Part Owner of the Ship. I was well treated by Capt. Read, and the Ship was very well provided with good and wholesome Provisions of several sorts, such as are carried to Sea; and I mess’d at the Captain’s Table, who lived very well, and eat fresh Provisions every Day…" (Uring, p. 1-2)
In the 1923 translation of German surgeon Johann Dietz's book Master Johann Dietz, Surgeon in the Army of the Great Elector and Barber to the Royal Court, the author reports,
"When the wind had abated itself we once more put to sea. Just at first I suffered a good deal in the flesh. But as I went to sea fasting and, as the custom was, took only a sup of salt water, which causes one to vomit immediately, it was soon all over." (Dietz, p. 147)
He does go on to give some suggested remedies. For example, after a trying bout of stormy weather he explains,
"Orders were shouted or sounded on the bell. But I was still unable to stand. Afterwards the bell was rung for work or meals, but the very smell of food made my gorge rise; for the caboose or galley stood not far from my mast. -At last I bethought me of a mixture of spiritus vitrioli [spirit of vitriol - diluted sulfuric acid - for more details, see my web page: http://www.piratesurgeon.com/pages/surgeon_pages/dispensatory25.html#sp_vitriol ], essence of violets and fresh water. I mixed this remedy for myself, and it did me good, so that I was soon on my feet again." (Dietz, p. 118-9)
He later suggests some other cures for sea-sickness: "The best remedy for this sickness is to chew pungent or aromatic spices, cinnamon, nutmeg, mace, black peppercorns, and so forth. Many think to cure the disorder by fasting, but in vain. Some drink sea-water, thinking thereby to make themselves vomit, but this is not due to the sea-water, but tothe aversion of the stomach from all food and drink." (Dietz, p. 292-3)
In his 1686 book Abstractum Chirurgiae Marinae, Sea surgeon John Moyle mentions sea-sickeness when he is discussing treatment of constipation. His comment suggests (although it doesn't directly state) that eliminating the constipation may help sea-sickness.
"Sometimes it happens that men are very Costive [constipated], or hard bound [extremely constipated]; or it may be there are passingers onboard, or delicate persons, that rather suffer a great deal of misery by this, than to take a Clyster [enema], especially such as are Sea-sick, and vomit much; I have known some who in a whole week together have not gone to stool: If any such complains to you, your way it so give him, either, Rx. Syr. De quincqu. rad. [Syrup of five roots - explained on my web page here: http://www.piratesurgeon.com/pages/surgeon_pages/dispensatory19.html#syr_five_roots] {2 ounces} or Tinctura solutiva [You can see William Salmon's recipe for this compound medicinal here: https://books.google.com/books?id=0KFgAAAAcAAJ&pg=PA465&lpg=PA465&dq=Tinctura+solutiva&source=bl&ots=GZK13NLkKr&sig=rB9os1iQpalZG87JqcmJtJVKYOM&hl=en&sa=X&ved=0CCEQ6AEwAGoVChMIibHJz_XGxwIVyJ6ACh3NCASK#v=onepage&q=Tinctura%20solutiva&f=false ]the like quantity." (Moyle, p. 111)