What is a good technique for making a very small amount of caramel?
You make small amounts the same way you make large amounts: dry or wet, doesn't matter, take your preference.
The problems you have are related not to the method, but to the wrong vessel. For example, for the dry method, you have to have the sugar neither too thick, nor too thin. For small amounts of caramel, you have to go with a small pot, possibly go down to 12 or even 8 cm (at least that's what works for me; if by &quot;tiny&quot; you really mean something like a tablespoon of caramel sauce, you might have to use a tiny vessel, like a muffin tin or a single portion cezve). The other desired quality is to have a vessel which provides even, measured heating, so a thick heavy bottom is always preferable.
Also make sure to use the right temperature, &quot;sugar gets burned while the rest is still dissolved&quot; sounds like you might be using too high heat.