Matthew Poole and continuators on Psalms 116:13

13 I will take the cup of salvation , and call upon the Name of the Lord .

I will offer the sacrifice of thanksgiving to God, as this phrase seems to be explained below, v. 17. where the latter clause of the verse is the same with that which here follows. The phrase is taken from the common practice of the Jews in their Thank-offerings, in which a Feast was made of the remainders of the Sacrifices, and the Offerers, together with the Priests, did eat and drink before the Lord, and amongst other Rites, the Master of the Feast took a cup of wine into his hand, and solemnly blessed God for it and for the mercy which was then acknowledged, and then gave it to all the guests, who drunk successively of it. See 1 Chron. 16. 2, 3. To which custom it is supposed that our blessed Saviour alludes in the institution of the Cup, which also is called the Cup of blessing, 1 Cor. 10. 16. which is in effect the same with the Cup of salvation. This Metaphor of a Cup is used both of afflictions, as Psal. 11. 6. & 75. 9. and of comforts, as Psal. 23. 5. Ier. 16. 8.

Or, publish or preach in or of the name of the Lord, i. e. his gracious nature and the great things which he hath done for me. For he speaks of praise rather than of prayer, as appears both from the former clause, and by comparing v. 17.