Some other suggestions here: http://typophile.com/node/70534

Psy-Ops foundry has a few.

Beorcana

I second Beorcana.
If it is only for display, have a look at Young Finesse.

This one unfortunately is all caps, but I believe I heard they were based on the same Italian inscriptions.

http://new.myfonts.com/fonts/letterperfect/donatello/

More of the original Italian look, but a nice font anyway by Paul Shaw.

You could also try a look through the stuff tagged as "flared" on MyFonts. Not everything there is relevant, but many are.

A ‘cuter’ Optima: Young Finesse

Stellar is the "original" Optima.

Magma by Sumner Stone

I second Young Finesse, Beorcana, and Magma.

Add to that list many Arthur Baker designs including Signet, Tiepolo, and Hiroshige, if you can use the ITC endomorphism.

Also http://Mentor Sans.

Strayhorn by Michael Harvey

I recently bought Stevens Percepta by Letterhead Fonts for display. It has a similar look but more character. I'm delighted with it. It has five weights and alternates for $49! - but no italic.

The kerning is extremely tight, I've had to increase in in most instances.

And although it isn't flared, Palatino Sans has much of the same character as Optima. Perhaps it's even a bit more informal.

Optima can certainly complement Palatino, in a rather obvious manner, as you infer.
They have similar letter forms, and a similar degree of gloss representing the trace of process: the flaring and concave terminals in Optima, and the flexed serifs of Palatino.

If you are prepared to focus more on that surface element of style, rather than the letter proportions, you might consider faces such as Laudatio or my Brown Gothic.

The most beautiful Optima-ish looking typeface I've seen is the type created for the new Statoil logo, however, I'm not so sure its for sale. If its for a logo only, you might want to just customize Optima to your liking.

Why not add PTL Publicala
http://primetype.com/faces_info.php?fid=45
(check the PDF)

If you can wait a little more I am releasing 2 free typefaces, one of them is CHIQ which you might be interested in. It has 3 weights (Regular, Medium, Bold) italics still in progress.

CHIQ is beautiful! I love the K and B, the graceful g, and the ampersand which looks flirty compared to the dignified letters.

The lc g is important to me. Many times I've decided not to buy a font cause I felt the g was ugly.

I thought that Tiepolo and Hiroshige had been designed by Cynthia Hollandsworth, not by Arthur Baker ?

@Celeste: according to the somewhat contradictory information on MyFonts, Hiroshige was designed by Cynthia Hollandsworth, while Hiroshige Sans by Arthur Baker.

Love that Q! Really nice alienbreed!

Yes, the Q is great. But what's that Caslon-like ampersand doing there? Looks like it doesn't belong.

Font Bureau - Amira