I was impressed by the Queen's expression of personal faith in Jesus Christ at the end of this video.
The 1662 Book of Common Prayer invites us to pray for the Queen in the following manner:
O Lord our heavenly Father, high and mighty, King of kings, Lord of lords, the only Ruler of princes, who dost from thy throne behold all the dwellers upon earth: Most heartily we beseech thee with thy favour to behold our most gracious Sovereign Lady, Queen Elizabeth; and so replenish her with the grace of thy Holy Spirit, that she may alway incline to thy will, and walk in thy way: Endue her plenteously with heavenly gifts; grant her in health and wealth long to live; strengthen her that she may vanquish and overcome all her enemies, and finally after this life she may attain everlasting joy and felicity; through Jesus Christ our Lord. Amen.
And here is an appropriate prayer for the royal family, especially in consideration of Prince Philip's current health condition:
Almighty God, the fountain of all goodness, we humbly beseech thee to bless Philip Duke of Edinburgh, Charles Prince of Wales, and all the Royal Family: Endue them with thy Holy Spirit; enrich them with thy heavenly grace; prosper them with all happiness; and bring them to thine everlasting kingdom; through Jesus Christ our Lord. Amen.