This is a fragment.
So, this is a sentence fragment, not a complete sentence. What makes this non-sentence look like a sentence is the use of participles and dependent clauses.
At this point you are now thinking, "Oh, right, participles, I think I remember those," or, "What is this 'participle?'"
Well, a participle is basically a form of a verb that works in a sentence like an adjective and so is considered to be one. Verbs ending in -ing are participles. Because a participle is working like an adjective, it cannot be the verb of a sentence. There has to be another verb, often a form of to be (e.g. is, was, am).
Not a complete sentence:
The running dog.
A complete sentence:
The dog is running.
So let's look at your fragment and break it down into individual phrases/clauses:
"Waiting for her to answer"
"his knees knocking"
"his brain considering rapidly
"what to say"
"when she did answer."
Right away we can eliminate three of those phrases because they contain participles without any other verbs.
"What to say" and "When she did answer" do contain verbs that are not participles, but they are still not independent clauses, i.e. are able exist as the backbone of a sentence. We can tell this by looking at the function each phrase serves.
"What to say" is not functioning as an independent clause. It is functioning as the object of another clause (so, a part of the predicate). Normally we learn objects as single nouns, such as in "He throws the ball." But look at "He considers what to say." Is it really so different? The ball is what he is throwing, what to say is what he is considering, and both are acting as objects, not able to be independent sentences.
In "what to say," we saw how multiple words can act like a single noun (called noun clauses by English teachers). In "when she did answer," the same thing goes, but this time all the words work as an adverb (called an adverb clause). Remember that an adverb basically describes how, when, why, etc. a thing happens. Again, we usually learn adverbs as single words, but a clause can act as one. "I'll answer soon." "I'll answer when she calls." Both describe when the calling happens, so they act like adverb, and "when she calls" cannot be its own sentence just like "soon" cannot be its own complete sentence.
None of the components of this sentence contain a main verb, so this is a sentence fragment.