Keeping up with opera screened in movie theatres is tricky - different cinema chains., different distributors, minimal publicity. Now here's help!
Check out the Bachtrack site (listed on the right of this page for easy reference. It's the best site for planning your schedule - everything in the same place, including things off the beaten track (Like Westminster Cathedral Dream of Gerontius). I use it all the time.
They've got details of Royal Opera House and NY Met screenings plus also Opus Arte European opera, most of which is top notch. More soon, too. Like Berlin Deutsche Oper's new season which features some of the top stars, including Joyce DiDonato,Jospeh Calleja, Jonas Kaufmann and this year's hot property Vittorio Grigolo - although you'll have to look through the listings carefully as they often have different casts for different nights of the same production. As well as the established repertoire, they are making a point of producing some lesser known operas such as Strauss's Die Liebe der Danae and Cassandra and Respighi's Marie Victoire.
When you're using the main "find an opera" or "find a ballet" pages, look out for one or more yellow bubbles at the top of the listing results: these will tell you if there are any cinema or on-demand listings which match your search.
Opera on film is different to opera live or on audio recording. Much depends on the musical intelligence of the film-maker. Some, like Brian Large, can turn trash to (almost) gold. Gone are the days when stand and shoot was enough - the camera has to follow the detail in a meaningful way. Long term there are implications for stageceraft because film opens possibilities not practicable in live performance. Certainly there are implications for the experience of opera, since audiences anywhere will get to see top quality shows. The end of one-city, one-house insularity. When people are actually exposed to things they've only read about before, perhaps they'll have more progressive attitudes. Some of the hysteria about "Regie" might dissipate when people realize the word simply means "directed". In French and German it's just a word but to some English-only speakers it's red flags to bulls.