I need to refer in Latin to the modern practice of 'tipping' in return for good service. I am well aware of words and phrases for 'reward', which are essentially correct for my purpose, but I should like, if possible, something both specific and authentically classical, and wonder if there is any reference to such a practice?
It seems that corollarium was used in this sense. Lewis and Short describe the original meaning as "money paid for a garland of flowers", but elsewhere it is described more like money put in a garland "and so a free gift" (editor's note on Lucilius, Satires, 12.464).
However, here Seneca uses it in the sense of tipping for services rendered:
Sordidissimorum quoque artificiorum institoribus supra constitutum aliquid adiecimus, si nobis illorum opera enixior visa est; et gubernatori et opifici vilissimae mercis et in diem locanti manus suas corollarium adspersimus.
If the hawkers of even the meanest forms of service seem to us to have put forth unusual effort, we give them something besides what we have agreed upon; we dispense gratuities to a pilot, to a man who works with the commonest material, and to one who hires out his services by the day.
On Benefits, 6.17, (trans. John W. Basore)
It's often held that the practice of tipping began in England around the 16th century, but there's some difference of opinion on the subject. For example:
There are a few versions for the origin of tipping. Hemenway (1993) claims that tipping was known as far back as the Roman era and is probably much older. Schein, Jablonski and Wohlfahrt (1984) assert that tipping originated back in the days of feudal lords. When lords met groups of beggars along their way, they tossed the beggars coins in an attempt to buy a safe passage. It is arguable, however, if this kind of payment should be considered tipping. Segrave (1998) suggests that tipping may have begun in the late Middle Ages. (Ofer H. Azar, "The history of tipping", 2004)
David Hemenway makes the following claim:
Popular belief holds that tip derives from eighteenth-century English usage and stands for the words 'to insure promptness,' but tipping was known as far back as the roman era and is probably much older. The word tip itself may come from stipend, a bastardized version of the Latin stips meaning gift. (Hemenway, Prices and Choices, 1977, p.77)
For this word stips, Lewis' An Elementary Latin Dictionary has the following:
(stips) stipis, f — STIP-, a contribution in money, gift, donation, alms contribution, dole. ne quis stipem cogito, lex ap. C.: stipem sustulimus, i. e. begging: stipem Apollini conferre, L.: stipis adice causam, O.: suburbanum hortum exiguā colere stipe, Cu.
Cicero used this word in De Legibus:
Praeter Idaeae Matris famulos eosque iustis deiubus, ne quis stipen cogito.
Which has been translated as "No one shall ask for contributions except the servants of the Idean Mother, and they only on the appointed days." In another part, he says:
Stipem sustulimus, nisi eam quam ad paucos dies propriam, Id matris excepimus, implet enim superstitione animos, et exhaurit domos.
I'm guessing that this word might be well-suited for your purposes. However, I think it still remains doubtful that its meaning is the same as that of tipping, i.e. as a gratuity for services rendered. As the following entry from A Compendious Dictionary of the Latin Tongue shows, it was used in the sense of a gift or offering (often in a religious context), as well as for the begging of alms:
I first had in mind the word mercedula, which is used in this sense — though it's fairly rare — and I asked the question thinking that I might find something rather better. In two excellent replies I have found stips and corollarium, each quite unknown to me. Gratias ago utrique.
Since stips seems mainly (wholly?) used for religious gifts, it has less appeal than corollarium, which in Penelope's answer is also in fact paid among other examples for a maritime service and therefore quite apposite to the passage for translation, which was:
"It was an old fisherman who, with immense difficulty, at last rescued us . . . . . What between tipping the man who had brought us home, and paying for the broken sculls . . . . . " (Jerome K. Jerome, 'Three Men in a Boat').