There's a very extensive medical literature - although mostly focusing upon persistent (>48 hours) or intractable (>1 month) hiccups. One possible remedy jumped out at me from Google Scholar results: title alone gives the game away (albeit N=1):

Odeh, M., Bassan, H., & Oliven, A. (1990). Termination of intractable hiccups with digital rectal massage. Journal of internal medicine, 227(2), 145-146.

A very recent review by Steger et al (2015) gives good coverage of "state of the art" in acute hiccups:

In acute hiccups, physical manoeuvres are often effective (Table 2). Many of these ‘remedies’ have not been tested and some appear to have been invented ‘purely for the amusement of the patient's friends’.[23] The principle that links these manoeuvres is the attempt to interrupt or suppress the reflex arc (Figure 1) thought to maintain repetitive diaphragmatic contractions.[8, 12] This is most often attempted by breath holding, the Valsalva manoeuvre or rebreathing into a paper bag. Physiological studies have demonstrated a mechanism by which these manoeuvres improve hiccups, with the frequency of hiccups decreasing as arterial pCO2 rises.[9] This experimental evidence, backed up by personal experience of the senior author, suggests that an effective method to interrupt hiccups is to hold ones breath in expiration (diaphragm relaxed, pCO2 high). Other techniques that can lead to cessation of hiccups involve stimulation of the nose, ear or throat (e.g. ice cold drinks), eyeball pressure, carotid massage or self-induced vomiting. Techniques that ‘push against’ the diaphragm by drawing up the legs to the chest (i.e. ‘rolling into a ball’) may also be helpful. Rectal massage and sexual stimulation have also been reported to help[24, 25]; however, we recommend that this kind of recommendation is reserved for carefully selected patients!

before concluding in case of persistent/intractable hiccups:

This systematic review revealed no high quality data on which to base treatment recommendations.

Steger, M., Schneemann, M., & Fox, M. (2015). Systemic review: the pathogenesis and pharmacological treatment of hiccups. Alimentary pharmacology & therapeutics, 42(9), 1037-1050.

Further note: reference [23] above in Steger et al (2015) is "Watterson B. The Complete Calvin and Hobbes. Kansas City, MO: Andrews McMeel Publishing, 2005."

Well, I know of some remedies, but they're also anecdotal :)

All the good ones I know are essentially breathing exercises, where you have to pay close attention to your breathing for a while (i.e. take control of your diaphragm). Like the classic "drink a glass of water from the far side of the glass" is actually a breathing exercise, which works just as well if you just do the breathing without the glass of water.

agree with others; the diaphragm is the muscle underneath the lungs that controls your breathing. Hiccups are caused by irritation of the diaphragm. knowing this; you are looking for methods of relaxing the diaphragm. that includes generally trying to work out the control for the automatic muscle; and figuring out how to calm it down.

as for trustworthy, or better-than-anecdotes - you can get surgery if it's a long-term (over several months) problem. how do you relax the diaphragm? for your human-hardware? likely different to other humans' hardware - so not much luck finding non-anecdote solutions.

This works for me: Pour yourself a glass of water and hold it in one hand. Lift your arms up, reaching for the ceiling - this movement has the consequence of lifting your ribcage. Drink a few swallows from the glass of water without dropping your ribcage from its elevated orientation. Do this a few times.