I went through the English WR dictionary and looked at all of the words that started with 'ce'.
"Cello" and "cembalo" are the only ones I could find with the 'ch' sound.
But these are not actually English words. Cello is from violoncello an Italian word.
Cembalo is also Italian.
"Celt" and "Celtic" would be with a 'k' sound.
Keep in mind that there are different pronunciations in BE.
I've heard 'cephalic' pronounced as 'kephalic'.
Concerto is another common one (the second C), and the food fettuccini (a kind of pasta). All of them are from Italian, and the C comes before E or I. There are several other less common musical and artistic terms – ricercar and cinquecento come to mind, words you'll never need to know unless you're a musician or art historian – and there could be a style of coffee or ice cream or something like that, also from Italian, though I can't think of any.
Other words borrowed from Italian where the "c" is followed by "e" or "i". chicken cacciatori, limoncello liquer, concerto, bocce ball, ciabatta bread, capuccino, ciao
It sometimes becomes "sh" after an "s".
Edit: entangledbank beat me to concerto, so I'll add an ice cream: stracchiatella