One of the most important things a singer must learn is that in order to actually keep the voice working correctly, and sounding even throughout the range, you have to actually allow the voice to change. If you keep the voice the same throughout the range it will not be even. This is a paradox for the beginner, and often even for the seasoned singer.
As the tenor (and this applies to other voice types) moves from low voice to high voice, there is a change in the way the voice works as more head tone comes in to it. This is not an uncommon idea right? The problem I have noted most in singers is that they often use the voice in very unnatural ways.
Bottom line is this: if you sing and then you speak in the same mode you are singing and your voice sounds encumbered by a weird tongue tension, or a narrow throat, etc., then you know you are doing things wrong. The voice should flow with the same natural delivery that it has when speaking. This has nothing to do with its resonance, it has to do with the correct connection between voice and breath and the absence of unnatural tensions which would cause your voice to become limited in its ability to say the musical phrase.
As obvious as this may seem, most singers fail miserably at this, so don’t give for granted that what you read is something you can do. This is particularly true as one ascends in range. Often tenors do all sorts of crazy things to secure high notes. Just speak on those tones and see if it sounds anything close to the natural delivery you would have in speaking. Sure it will be high pitched, and somewhat effeminate or boyish and bright, but it should flow naturally like normal speech would.
Here is an audio clip explaining these same things: