Luke 1:4
That thou mightest know the certainty of those things, wherein thou hast been instructed.
Cross-reference
John 20:31
Parallel
John 20:31 states his purpose 'that you may believe' — Luke's purpose is 'that you may know the certainty', both gospel writers giving explicit reasons for writing.
2 Peter 1:16
Parallel
2 Peter 1:16 rejects 'cunningly devised fables' and appeals to eyewitnesses — Luke's certainty similarly counters doubt, grounding truth in careful investigation.
Proverbs 22:21
Allusion
Proverbs 22:21 says 'that you may know the certainty of the words of truth' — Luke almost quotes this exact phrase, borrowing the language of wisdom to guarantee his account.