The obvious way to nudge people toward Christlikeness is to preach about Christlikeness. You take a passage and then what do you look for? You might look to find any instructions, derive some applicational points, determine how Christ’s character is presented, identify some kind of divine demand, etc. Essentially, the obvious way to promote Christlikeness is to present Christlikeness and encourage Christlikeness in your listeners. Focus on character, focus on us. Apply, exhort, encourage.
There is a better way.
Turn the words around. Do your listeners like Christ? Do you? Christ did not come to the world merely to show us a new way to live. He came to give us life in union with Him. The life of the Trinity is given to us in Christ. This means that Christlikeness will not flow primarily from Christlikeness explained and demanded. Christlikeness will come from liking Christ, from loving Him, from knowing and worshipping Him.
Preach so as to present Christ. Offer the person of Christ rather than a programme for self-improvement. Invite people to know Him and to love Him. As the Spirit draws people to Christ, they will grow to like Him and to live like Him. As the text you are preaching presents instruction, then offer that faithfully in the context of relationship with Christ.
Christlikeness isn’t the goal of preaching for sanctification, it is the fruit. The goal must be to stir greater love for God that results in greater love for others, and love will be stirred not by demand, but by presentation of God’s love revealed in Christ. Inasmuch as we like Christ, we will grow to live Christ-like lives.