It’s very easy to tense up the tongue, jaw, and/or throat when you’re fine-tuning your pitch accuracy: you may end up with better intonation but also a pinched tone, and possibly vocal fatigue. Here’s a method that can help:
1] Work with Hearfones so you can hear yourself as well as the track or instrument to which you are tuning. A mic and headphones will work, too. More info on Hearfones is on their site, but they are usually cheaper at Amazon.
2] Massage the sides of your neck and perhaps your shoulders and jaw as you sing. DO NOT directly massage your larynx (behind your Adam’s Apple), that area is too delicate. It can be tricky to fit your fingers around the Hearfones but it can be done. You can also try swaying as you sing to stay relaxed.
3] Work with some kind of track or instrument when you’re doing this kind of work, not a cappella. It’s too easy to stray from the key when singing a cappella.
4] Record yourself periodically to fine-tune your vocal more.
For most singers singing in tune is an ongoing project-- it's not something you just work on for awhile and then are set for life. So don't worry if periodically you need to do more intonation work.