Coscinomancy

Meaning: Divination by the sieve and shears. It's difficult to explain, but Brewer claims that:

The points of the shears were stuck in the rim of a sieve, and two persons supported them with their finger-tips. Then a verse of the Bible was read aloud, and St. Peter and St. Paul were asked if it was A, B, or C (naming the persons suspected). When the right person was named, the sieve would suddenly turn round. 

The first image here will give you an idea of the fragility of the arrangement on which someone's guilt might rest.

Usefulness: 2 (Mainly as a synonym for a pointless, arcane ritual that confirms what everyone suspects. Elections, perhaps?)

Logofascination: 3 (I'm more fascinated by the weird and wonderful ways humans have sought for truth.)

Capricious

Meaning: You probably already know the meaning of this word, but Cotgrave defines caprice as:

A humor, caprichio, giddie thought, fantasticall conceit; a suddaine will, desire, or purpose to doe a thing, for which one hath no (apparent) reason.

I rather like the cynicism of that (apparent). Caprichio was a synonym for caprice, but now survives only in music.

Usefulness: 1 (Although if you wish to substitute giddie thought from now on, I won't blame you.)

Logofascination: 1 (It's a goat word! Probably! In fact, according to etymonline it's either from the Latin for wild goat, or a word about people with curly hair, and how can you not love that? I had a lightbulb moment when someone at work used it this week, and unlike a lot of etymological lightbulbs, this one was correct! Probably! Goats have a suprisingly strong influence on etymology, so I'm erring in their favour.)

Mastigophorous

Meaning: whip-bearing; used humorously* of British schoolmasters.

Usefulness: 1 ("Morning boss; looking particularly mastigophorous today." "You should all know that my approach to this year's budget will be mastigophorous."  Can obviously also be applied to jockeys, rodeo riders and other less savoury occupations.)

Logofascination: 1 (From the Greek for 'whip' and 'carrying', it's the sort of word Sir Thomas would have invented.)

Calefaction

Meaning: warming and heating, or being warmed and heated.

Usefulness: 1

Logofascination: 1 (Rabelais has the French échauffer, but Sir Thomas uses the English calefaction, which is from the same Latin root. Perhaps his coinages occurred where he felt he needed an equivalent to the French he was translating.)

Paroemiographer

Meaning: a writer or collector of proverbs.

Usefulness: 1 (I'm considering adding this to my resume. Could also be applied to Twitter, where there are a number of people attempting to find or coin the most applicable proverb of the day.)

Logofascination: 2 (This word gets points just for existing.)

Astragalomancy

Meaning: divination using the huckle-bones (a small bone around the ankle, I think) of sheep; apparently these days people have gone soft and use dice instead.

Usefulness: 3 (Unless you're on a sheep farm. Or in New Zealand.*)

Logofascination: 1 (The name comes from the Greek astragalus, their name for the bone, which also gives us astragaloid and astragalize, the latter meaning to play at dice.)

Enixibility

Meaning: the possibility of being born - the OED says "?* Possibility of being brought forth".

Usefulness: 2 (Could be quite useful in the film industry: "Hugh Jackman's signed on, which automatically triples the enixibility.")

Logofascination: 1 (From enixus, a word to do with struggling which came to mean giving birth.  The OED takes the rather unusual step of listing enixibility as a "nonce-wd. (bombastic.)". The application of 'bombastic' to nonce-words seems to turn up only in a small patch around D and E.)