When I was growing up, I remember thinking that they had arranged marriages in Japan, probably something I got from watching the episode of Happy Days where Arnold gets married in a traditional Shinto wedding ceremony — not the best place to get information on other cultures. In reality, they have “arranged meetings” called omiai, a kind of formal meeting between prospective partners, usually organized by busybody aunts who can’t leave well enough alone. At an omiai, both parties talk about their interests and background and if they hit it off, they go out on more conventional dates to see where things lead. Before my wife met me, she had had omiai meetings with a few men, for example the son of a sake distributor that our liquor shop buys from that her parents wanted her to marry — fortunately for me she didn’t hit it off with any of them. As time marches on, the old-style formal omiai meetings are giving way to more modern methods, with companies and even manciple governments organizing “omiai parties” (gatherings of marriage-minded people who interact with each other in a fixed space).
Omiai are not common in anime, except for Maison Ikkoku.