You can get around that by using harmonics. Because you play harmonics without pushing all the way down, you can achieve a more precise tune.
The strongest harmonic is achieved when you gently place your finger on the string directly over the metal fret. A harmonic can only be achieved when you do not press the string all the way down into the fret.
The harmonic on the 7th fret of one string is the same note as the harmonic on the 5th fret on the next higher string. This is true for all consecutive string pairs other than (G, B).
You can tune using these pairs of harmonics to tune more precisely than pressing all the way down.
You will need to tune the (G, B) pair without harmonics.