I recently remembered a book I read and loved as a child.  This was
around 15 years ago, so the book is at least that old.  It's about a
witch.  She lives in a castle or other large building (the book said
she kept a small apartment in the castle)  The plot of the book is her
cat goes missing.  She is friends with this "king" who will help (she
says he "owes me a favor or two).  I'm not 100% sure he's a king - he
is someone powerful, he owns jewel mines.  The witch has 3 people who
acompany her on her search for her cat.  One elf-sort-of-thing, and 
boy and girl.  The elf (again, not 100% sure it's an elf, but it's not
human) is jealous of the witch's relationship with the boy and girl,
and gets all them arrested by stealing jewels from the "king's" jewel
mine. (He pulls emergency cord on the train, and plants the jewels on
the boy and girl)  Then the witch and company have to go on some
"quests" to get the king to help her find her cat.  The ending is the
fuzziest part for me, but I seem to recall the witch comes home and
find her cat there - it had kittens.  I could be completely wrong
about the ending.

Anyway, I would love to find this book again - any help about the
author or title would be much appreciated.  Thanks!

Hello.

Your book is probably "Witches, Ghosts, and Goblins; A Spooky Search
for Miranda's Cat" (1974) written by Ruthanna Long and illustrated by
Paul Durand.

See this description of the plot from the Library of Congress catalog:
"Polly and Oliver's attempts to help a friendly witch recover her lost
cat take them to the Land of the Goblins, Ghost Valley, Witch City,
and other extraordinary places."
For more information about the book, see the Library of Congress
catalog entry:
http://catalog.loc.gov/cgi-bin/Pwebrecon.cgi?v3=1&DB=local&CMD=010a+72093996&CNT=10+records+per+page

Several used copies are listed for sale on Alibris.com:
http://www.alibris.com/search/search.cfm?qwork=7255671&matches=4&qsort=p

Abebooks.com also lists several copies:
http://dogbert.abebooks.com/servlet/BookDetailsPL?bi=149452402
http://dogbert.abebooks.com/servlet/BookDetailsPL?bi=144500590

search strategy: witch, "her lost cat"

I hope this helps.

Very helpful.  Thanks so much!  (Although it's sad this books is so
expensive - wow!)