The news that Senator Barack Obama will be visiting his ailing grandmother in Hawaii gave me the idea to talk a bit about お見舞い (おみまい omimai) vs. お見合い (おみあい omiai), two very similar sounding words with very different meanings, both of which give some insight into Japansese society.
Visiting someone who's ill
お見舞い (おみまい omimai)means to visit someone who is not well, most often someone who is hospitalized (入院 にゅういん nyuuin, to be hospitalized) in a 病院 (びょういん byouin , hospital), though you can お見舞い someone who is sick at home or in a rest home too. (お見舞い is the honorific version of 見舞い, but お見舞い is almost always used. It's a noun, and to turn it into a verb you use お見舞いする omimai suru, to do omimai).
When you お見舞い someone in hospital, you usually bring them flowers or fruits and so on just like in the west. It is rather bad form to go visit someone in hospital empty-handed, when it's the first time you are going there. You shouldn't bring a potted plant, since that implies the hospital stay might take root (根付く ねづく nezuku - to take root, sounds the same as 寝づく - stay bed-bound) and be prolonged. Cut flowers are ok.
The arranged first date
On the other hand, お見合い (おみあい omiai) is an arranged meeting with a prospective marriage mate. Even in 2008, many people still do お見合い to meet their future mate. You first get a photo and a sort of life-resume of the potential お見合い candidate, and decide whether you want to meet them. The お見合い itself is usually held at an expensive restaurant, Western or traditional Japanese style, with each party bringing along a chaperone. The first part of the meeting is with all four people, then later the young couple are let alone for a bit. After the お見合い、if both sides decide they want to pursue the relationship they do.
I've never done an お見合い myself since I've lived most of my adult life outside Japan. (お見合い do occur between Japanese people living abroad, but very rarely.) I've heard some funny or horror stories of お見合い from other people though, such as a girl who had an お見合い with a guy with all the 'right' credentials - Tokyo University graduate (the ultimate in prestigious degrees, which is very important in Japan), in a top rated big corporation, even not bad looking. His chaperone was his mother, which is not that unusual, but during dinner he called his mother "Mama", while she in turn called him (his name)-chan (a diminutive term of endearment usually used for little children). "Mama" chose his menu and at one point even wiped his mouth for him! My friend didn't pursue the relationship, needless to say.
While you can have some nightmare お見合い、I don't think it's such a bad or outdated idea - it's just a formal kind of blind date. But it is going out of favor amongst younger Japanese people, who prefer the Western romantic ideals of chance encounters.