The concept of "capitalization" is not part of the official IPA
The official chart showing the International Phonetic Alphabet is downloadable from the IPA website. IPA letters are not defined in cased pairs. Most of them look like lowercase letters (and I believe are treated as lowercase letters in Unicode encoding; I don't know if there are any exceptions to that). Some look like small caps; these are just separate letters, representing separate sounds. (Usually the sound is similar in some regard to the source letter, but there is no single rule connecting the sound of an IPA letter that looks like a Latin alphabet small-caps letter to the sound of an IPA letter that looks like the "corresponding" Latin alphabet lowercase letter.)
Obviously, the IPA letters a, b, c... z, which are identical to letters of the familar Latin alphabet, have upper-case equivalents A, B, C... Z in the context of the larger set of Latin alphabet characters, but these upper-case equivalents are not formally defined as part of the IPA, and there is no common informal use for them in phonetic transcriptions that I know of.
Use of capital letters in some phonological transcriptions
In phonological transcriptions, full-sized capital letters of the Latin alphabet may be used in a way Typhon mentioned in a comment below:
I have seen upper case used to denote archiphonemes in broad transcriptions. I'm not sure if it's standard practice. – Typhon
I would say this still isn't exactly "capitalization" because the capital letters don't correspond to a single lowercase IPA letter, but to a set of them (e.g., N might be used as a symbol representing the neutralization of both /n/ and /m/).
Also, a transcription with archiphonemes is fairly definitely not phonetic (I don't mean to say that there is a clear line between phonetic and phonemic transcriptions, just that I think most people agree that no matter how blurry the line is, archiphonems are on the phonemic side, and maybe even beyond it i.e. on a "third" level).
Use of capital letters in some practical orthographies based on the IPA
The practical orthographies of some languages contain letters taken from the IPA (or from other similar phonetic transcription systems), and in this context, capitalized/uppercase letters often may occur. But these are not official IPA, just similar but distinct scripts. There are even some upper-case equivalents to certain letters of the IPA outside of the 26 basic Latin ones: while these uppercase forms are not part of the IPA, they are used in some alphabets like the "Africa Alphabet" (which has Ʃ as the upper-case form of ʃ, Ʒ as the uppercase form of ʒ, Ŋ as the uppercase form of ŋ, and some others).
In the case of the glottal stop letter <ʔ>, there is some variation. It is used as a case-invariant letter in the orthographies of some languages, but there is also a pair of derived characters that are used as a cased equivalent in the orthographies of some other languages: uppercase <Ɂ> and lowercase <ɂ>.
You can see more examples at the Wikipedia article Case variants of IPA letters