This promise, from the prophet Isaiah, follows from one of the major prophesies about the Messiah, Jesus!
"Comfort ye, comfort ye my people, saith your God.
2Speak ye comfortably to Jerusalem, and cry unto her, that her warfare is accomplished, that her iniquity is pardoned: for she hath received of the LORD'S hand double for all her sins.
3The voice of him that crieth in the wilderness, Prepare ye the way of the LORD, make straight in the desert a highway for our God.
4Every valley shall be exalted, and every mountain and hill shall be made low: and the crooked shall be made straight, and the rough places plain:
5And the glory of the LORD shall be revealed, and all flesh shall see it together: for the mouth of the LORD hath spoken it." (Isaiah 40: 1-5)
"1But they that wait upon the LORD shall renew their strength; they shall mount up with wings as eagles; they shall run, and not be weary; and they shall walk, and not faint." (Isaiah 40: 31)
"Wait" in the above verse is better rendered as "hope" or "trust in".
Today, we have Christ Jesus living in us by His Spirit, and we can know and believe in His love for us, that He is holding us in His hands:
"My Father, which gave them me, is greater than all; and no man is able to pluck them out of my Father's hand." (John 10: 29)
Now, what is the basis for this precious promise? Righteousness!
"I will uphold you with my righteous right hand," the LORD promises.
Today, we have been made the righteousness of God in Christ (2 Corinthians 5:21), and we can rest assured that we are established in His righteousness:
"4In righteousness shalt thou be established: thou shalt be far from oppression; for thou shalt not fear: and from terror; for it shall not come near thee.
. . .
17No weapon that is formed against thee shall prosper; and every tongue that shall rise against thee in judgment thou shalt condemn. This is the heritage of the servants of the LORD, and their righteousness is of me, saith the LORD. (Isaiah 54: 14, 17)
We can rest assured that we are OK, that we are safe in His hands, because of His righteousness.