Kilner jars are rubber sealed screw-top glass jars first made by the Kilner family in Yorkshire. The real trick to them is their two-part lid - a metal screw band & separate rubber-bottomed metal lid. This ingenious little system means that air can escape when processing, but not get in (bringing its friends bacteria & micro-organisms). You can process all sorts of fruits in syrup or brine using kilner jars, but vegetables are a bit more complicated. The biggest concern when dealing with tomatoes is the dread botulism, but if you're careful with keeping things sterile & clean, you shouldn't have anything to worry about. Acid prevents botulism spores from developing, so adding a tablespoon of lemon juice or vinegar (red wine or balsamic really brings out the flavour of tomatoes) should solve any problems. Bringing the passata to the boil for 10 minutes when using will also kill off anything nasty (and, of course, not eating anything from a jar that is bubbling or fermenting, turned a funny colour, gone mouldy or is attempting to communicate with you is also a smart move).
There are two methods of preserving in kilner jars - the Water Bath method & the Oven Method. Both methods need clean, sterilised jars (and work with screw top & clip top jars) filled with hot passata leaving a 2cm gap at the top, but you already know that.
The Water Bath is the most common method. For this you need a pan deep enough to keep your jars completely submerged, a large preserving pan works well. You'll also need a thermometer. Place a folded tea towel on the base to protect the jars from the direct heat(they will crack otherwise). Fill the jars with hot passata (about 60C) and srew on the lids, loosening by a quarter-turn (to give steam a chance to escape). Place the jars in the pan & cover with warm water. Slowly bring to a simmer (I mean slowly. Take about 20-30 minutes over it. You don't want a pan of watery tomato & glass shard soup) & simmer at 88C for 40 minutes. Remove from the heat & stand on a wooden board or folded towel, tighten up the screw bands & leave to cool overnight. In the morning check the seal (the dimple in the top of the jar should have depressed, and alarmed you at some point in the evening with a loud pop!). If there is no seal, either use up immediately or process again.
Te Oven Method takes longer, and can get a bit messy, as the passata will bubble & spit while its in the oven, but doesn't require a big preserving pan. Preheat the oven to 150C/300F/G2. Fill the jars & place on a thick pad of newspaper, or a folded tea towel in a baking tray filled with 3cm of water (to disperse the heat, and prevent any distressing breakages. Place the jar lids on top, but don't fasten with screw bands. Leave in the oven for 60 minutes, then carefully remove, clean off any tomato that has escaped & put on the screw bands tightly. Leave to cool overnight & check the seal. Store in a cool, dark place (i.e. a cupboard) for up to a year.