I'm trying to locate a story I read sometime in the early 2000s, but I believe it was published in an anthology from decades earlier (1960s-1980s). The story involved a date or sexual encounter between a man and a woman on a space station. Even though they have known each other for only a brief time, they decide to "get married," which simply means scanning each other with advanced technology (holographic? nanotech?) that allows them to store a copy of the "spouse" on some kind of recording device. The "spouse" can be conjured up, whenever desired, as a hologram or digital projection of some sort.
This sounds like the 1966 short story "Day Million" by Frederik Pohl (wiki link is for the anthology of that title but contains a summary of the title story as well), that has been anthologized several times (including the originally-from-1979 collection, reprinted in the early 2000s, "The Road to Science Fiction Vol 3: From Heinlein to Here")
After a brief description of the couple, the author describes them meeting and almost immediately deciding to marry:
On Day Million Dora swam out of her house, entered a transportation tube, was sucked briskly to the surface in its flow of water and ejected in its plume of spray to an elastic platform in front of her—ah—call it her rehearsal hall. "Oh, shit!" she cried in pretty confusion, reaching out to catch her balance and find herself tumbled against a total stranger, whom we will call Don.
They met cute. Don was on his way to have his legs renewed. Love was the farthest thing from his mind; but when, absent-mindedly taking a short cut across the landing platform for submarinites and finding himself drenched, he discovered his arms full of the loveliest girl he had ever seen, he knew at once they were meant for each other. "Will you marry me?" he asked. She said softly, "Wednesday," and the promise was like a caress.
They do indeed marry by exchanging recordings of each other:
It is people that make stories, not the circumstances they find themselves in, and you want to hear about these two people. Well, they made it. The great thing they had for each other grew and; flowered and burst into fruition on Wednesday, just as Dora had promised. They met at the encoding room, with a couple of well-wishing friends apiece to cheer them on, and while their identities were being taped and stored they smiled and whispered to each other and bore the jokes of their friends with blushing repartee. Then they exchanged their mathematical analogues and went away, Dora to her dwelling beneath the surface of the sea and Don to his ship.
It was an idyll, really. They lived happily ever after—or anyway, until they decided not to bother any more and died.
Of course, they never set eyes on each other again.
And can call each other up at will:
She loves Don very much. She keeps his every gesture, mannerism, nuance, touch of hand, thrill of intercourse, passion of kiss stored in symbolic-mathematical form. And when she wants him, all she has to do is turn the machine on and she has him.
And Don, of course, has Dora. Adrift on a sponson city a few hundred yards over her head or orbiting Arcturus, fifty light-years away, Don has only to command his own symbol-manipulator to rescue Dora from the ferrite files and bring her to life for him, and there she is; and rapturously, tirelessly they ball all night. Not in the flesh, of course; but then his flesh has been extensively altered and it wouldn't really be much fun. He doesn't need the flesh for pleasure. Genital organs feel nothing. Neither do hands, nor breasts, nor lips; they are only receptors, accepting and transmitting impulses. It is the brain that feels, it is the interpretation of those impulses that makes agony or orgasm; and Don's symbol-manipulator gives him the analogue of cuddling, the analogue of kissing, the analogue of wildest, most ardent hours with the eternal, exquisite and incorruptible analogue of Dora. Or Diane. Or sweet Rose, or laughing Alicia; for to be sure, they have each of them exchanged analogues before, and will again.