John Piper says "we battle the unbelief of anxiety with the promises of God." He also shares these specific promises:
When I am anxious about some risky new venture or meeting, I battle unbelief with the promise: Fear not for I am with you, be not dismayed for I am your God, I will help you, I will strengthen you, I will uphold you with my victorious right hand (Isaiah 41:10).
When I am anxious about my ministry being useless and empty, I fight unbelief with the promise, So will my word that goes forth from my mouth: it will not come back to me empty but accomplish that which I purpose, and prosper in the thing for which I sent it.
When I am anxious about being too weak to do my work, I battle unbelief with the promise of Christ, My grace is sufficient for you, my power is made perfect in weakness (2 Corinthians 12:9), and as your days so shall your strength be (Deuteronomy 33:25).
When I am anxious about decisions I have to make about the future I battle unbelief with the promise, I will instruct you and teach you the way you should go; I will counsel you with my eye upon you (Psalm 32:8).
When I am anxious about facing opponents, I battle unbelief with the promise, If God is for us who can be against us! (Romans 8:31).
When I am anxious about being sick I battle unbelief with the promise that tribulation works patience and patience approvedness and approvedness hope and hope does not make us ashamed (Romans 5:3-5).
When I am anxious about getting old, I battle unbelief with the promise, Even to your old age I am He, and to gray hairs I will carry you. I have made, and I will bear; I will carry and will save (Isaiah 46:4).
When I am anxious about dying, I battle unbelief with the promise that none of us lives to himself and none of us dies to himself; if we live we live to the Lord and if we die we die to the Lord. So whether we live or die we are the Lord's. For to this end Christ died and rose again: that he might be Lord both of the dead and the living (Romans 14:9-11).
When I am anxious that I may make ship wreck of faith and fall away from God, I battle unbelief with the promise, He who began a good work in you will complete it unto the day of Christ (Philippians 1:6). He who calls you is faithful. He will do it (1 Thessalonians 5:23). He is able for all time to save those who draw near to God through him, since he always lives to make intercession for them (Hebrews 7:25).
People need to hear these promises when they are filled with anxiety. But we need to share these promises without having a simplistic "take two verses and call me in the morning" attitude - that is, we should strive to speak in a context of sensitivity, caring and understanding.
For further thoughts on dealing with anxiety, see of "Getting to the Heart of Your Worry," by Robert D. Jones, summaryThe Journal of Biblical Counseling, (vol. 17/13, Spring 1999).