NOTE: All examples below gleaned by creatively grepping the OED.
Whenever you create a brand new word by applying a productive prefix to a proper noun, which therefore begins with a capital letter, the hyphen is obligatory.
This general rule is especially useful for nonce words, coinages you create on the fly, which might not otherwise be recognized by the reader. When you create a new derived term where each part is normally capitalized, then with time, the hyphen and the second capital tend to become lost.
For example, we oppose the Arctic not with the *ant-Arctic, but with the Antarctic. And while terms like Tibeto-Himalayan or Proto-Indo-European seems resilient to this process, many others are not, including:
(There are also a few false positives to be wary of, like Bildungsroman and Künstlerroman, which do not, in fact, involve any Roman elements. :)
Counterexamples, where neither capitals nor hyphens remain, include:
- acatholic — a word the OED equates to non-Catholic
Some terms enjoy more than one attested spelling. The fully hyphenated and capitalized version tends to occur first historically, as the term is first coined and then popularized, while the smoothed-down version follows once the term has been around a while. So the Pre-Cambrian period of geologic time is now often spelt Precambrian, and the “European climatic period that followed the Arctic and preceded, or marked the transition to, the Boreal period, and was characterized by the spread of birch and pine forests is variously spelt Preboreal, pre-Boreal, and preboreal.