In his comments on Philippians, chapter 1, verse 6:

And I am sure of this, that he who began a good work in you will bring it to completion at the day of Jesus Christ. Philippians 1:6 English Standard Version (ESV)

John Calvin says:

It is asked, however, whether anyone can be certain as to the salvation of others, for Paul here is not speaking of himself but of the Philippians. I answer, that the assurance which an individual has respecting his own salvation, is very different from what he has as to that of another. For the Spirit of God is a witness to me of my calling, as he is to each of the elect. As to others, we have no testimony, except from the outward efficacy of the Spirit; that is, in so far as the grace of God shews itself in them, so that we come to know it.

There is, therefore, a great difference, because the assurance of faith remains inwardly shut up, and does not extend itself to others. But wherever we see any such tokens of Divine election as can be perceived by us, we ought immediately to be stirred up to entertain good hope, both in order that we may not be envious towards our neighbors, and withhold from them an equitable and kind judgment of charity; and also, that we may be grateful to God. This, however, is a general rule both as to ourselves and as to others — that, distrusting our own strength, we depend entirely upon God alone [emphasis mine].

And what can we look for as tokens of Divine election? Scripture says we are to be clothed in His righteousness, in word and deed:

Put on then, as God’s chosen ones, holy and beloved, compassionate hearts, kindness, humility, meekness, and patience, bearing with one another and, if one has a complaint against another, forgiving each other; as the Lord has forgiven you, so you also must forgive. Colossians 3:12-13 (ESV)

Look for these things in yourselves first and then in others.

Tamme-Lauri oak. The oldest tree in Estonia, 3 September 2013, Abrget47j, Creative Commons Attribution-Share Alike 3.0 Unported