Sayyidunā 'Uthman [may Allāh Almighty be pleased with him] was a very strict follower of the Sunnah of the Beloved Messenger of Allāh, may Allāh Almighty bless him and grant him peace, and was drowned in his love. He always feared Allāh Almighty and did nothing that would displease Allāh Almighty or his Beloved Prophet, may Allāh Almighty bless him and grant him peace. He would often cry due to the fear of Allāh Almighty, death, and the concern of the hereafter.

Bay'ah with the Messenger of Allāh, may Allāh Almighty bless him and grant him peace 
He loved the beloved Messenger of Allāh, may Allāh Almighty bless him and grant him peace, and all his blessed actions, to the extent that he did not let any impurity get on the hand with which he gave oath [bay'ah] to the Messenger of Allāh, may Allāh Almighty bless him and grant him peace.

Smiling after ablution 
He loved the Prophet, may Allāh Almighty bless him and grant him peace, so much so that he would observe all the actions and followed them. Once 'Uthman [may Allāh Almighty be pleased with him] smiled after Wudhū and was asked as to why he smiled. He replied, I saw the Messenger of Allāh, may Allāh Almighty bless him and grant him peace do the same. [History of the Khulafas, pg 30-31]

Follow me or leave me 
Sayyiduna Uthman [may Allah Almighty be pleased with him] spent his life practising even the smallest Sunnah of the Messenger of Allah, may Allah Almighty bless him and grant him peace, and gave invitation to others to practise the Sunnah. When he became caliph, he stood in front of the people and said, Follow me until I follow the Sunnah and leave me as soon as I leave the Sunnah. If I leave or move away from the Sunnah then show me the Sunnah of the Messenger of Allāh, may Allāh Almighty bless him and grant him peace. [History of the Khulafa, pg 32]

A passing funeral 
Once a funeral was passing Sayyidunā 'Uthman [may Allāh Almighty be pleased with him] when he suddenly stood up and said, The Messenger of Allāh, may Allāh Almighty bless him and grant him peace, would do this. [Adab of Sunnah, pg 31]
The mother of the believers, Sayyidā Ayesha Siddīqah [may Allāh Almighty be pleased with her] related that the beloved Messenger of Allāh, may Allāh Almighty bless him and grant him peace, gathered his garments around him when 'Uthman entered, and said to 'Uthman, Should I not feel shy of a man of whom the angels are shy? [History of the Khulafa, pg 162]
Glory be to Allāh Almighty! This is the Messenger of Allāh, may Allāh Almighty bless him and grant him peace, saying this, however, we do not feel shy at all when we go against the teaching of the Messenger of Allāh, may Allāh Almighty bless him and grant him peace. Oh Allāh Almighty! Give us the ability to follow in the footsteps of Sayyidunā 'Uthman [may Allāh Almighty be pleased with him.]