Well... since you asked... the LONG answer....
I calibrate my Tilt in tap water (city water). I suppose you can use distilled or RO water if you want to be super anal about it, but I think there's far more important considerations to be concerned with.
I had to zero (1.000) my Tilt like a dozen times before it really stabilized for good. I discovered this was because I used tap water which is aerated on the faucet itself, so there were tiny air bubbles that kept coming out of solution and clung to the Tilt and messed up the readings. So I found that after the water sat out for several hours, I could shake the tiny bubbles off and they did NOT come back anymore.
Also I tried very hard to get the Tilt away from the sides of the container of water, made sure it didn't touch anything. I'm concerned that if it touches the sides, water tension will mess up the readings. It takes a lot of work to keep the Tilt centered and away from the sides. Had to do that over and over. I'm honestly not sure if touching the sides is a bad thing, but I take no chances.
So ultimately, I know I got 1.000 at that calibration point.
Then meanwhile, you also need to do the same with a standard hydrometer so that you can zero that too and use it for all further comparisons. My old hydrometer always reads about 1.002 in plain water, so I know it's a little high and always have to subtract off 0.002. Very very important. If you don't calibrate your standard hydrometer, all your other Tilt calibrations are going to be screwed up.
On brew day, after you brew and you take your OG measurements, you need to use both the Tilt and the standard hydrometer together, then enter that into the Tilt software as another cal point. You could also do the same for pre-boil gravity, that would be another good cal point. Just be sure the temperatures are always 60-70 F (15-20 C). Temperature has a very significant effect on gravity measurements.
And then finally, when it comes time for FG measurements, you need to be aware IF there's some protein and hop matter stuck to your Tilt, it will definitely mess up the reading. The trick I've found here is that both during and after fermentation, if I shake the fermenter vigorously for a few seconds once or twice per day, it will keep the Tilt relatively clean so that it reads more accurately. People who don't do this will find their FG readings are way off compared to a standard hydrometer, but by removing most of the protein & hops you can still get it accurate within 0.001-0.002.
One thing I'm still not certain about is whether or how the Tilt compensates for temperature fluctuations. I get the feeling that it does seem important to get an accurate temperature on the Tilt in addition to the specific gravity so that it will maintain accurate SG at different temperatures. So I calibrate for temperature in much the same way as for SG, using multiple thermometers and take the average to try to get as accurate as I can. On the other hand, the Tilt is only good to 1.0 degree so don't fret if the Tilt says 68.4 F but your other thermometer says 68.9 F or whatever -- that's as close as you're going to get, and in fact it's very normal for the Tilt to then jump back and forth between 68.4, 67.4, 69.4, up and down by a degree or two from minute to minute because it is incapable of reading any decimal places in between, it can only jump a whole 1.0 if it think it senses a little change and feels the need to make a leap up or down. Yeah... temperature measurement with the Tilt is a little misleading, best you can really do is take an average of like a dozen readings over a few hours because at any given moment it might be off by a whole degree or more. Well, same can be said for SG I suppose as well.
Regarding thermometers, I calibrate my favorite thermometer in both ice water and boiling water CORRECTED FOR MY ELEVATION ABOVE SEA LEVEL (MIGHT NOT BE 212 F (100 C)!). I know my mash thermometer reads a little low at one point and a little high at the opposite point (I can't remember which), such that I know it reads fairly accurately in between within a degree. BUT, if you've never done this with your thermometer(s), then you really don't know how accurate it is then, do you!?
Yeah... the Tilt is a fun (but expensive!) little toy, and you can get really accurate results with it, IF you calibrate ALL your instruments with utmost care on your first batch or two. After that, it should work for subsequent batches....... until you need to change the batteries! So far I've used mine 3 times I think and it's still alive on original batteries. Crossing fingers for next time.