The second gift was the second-base bag from the final game at the now-demolished Hubert H. Humphrey Metrodome. Jeter's Yankees won that 2009 American League Division Series contest, 4-1.
"It's cool," Jeter said. "Everywhere I've gone, I've gotten some neat things, but they did a nice job. And then to have [Paul] Molitor out there, [Brian] Dozier out there [for the ceremony], these are the things I'll remember."
Jeter was 1-for-4 with a double in that final Metrodome game, and he collected at least one hit in all 14 postseason games he played against Minnesota (20-for-57, .351) to go along with three home runs and eight RBIs.
The future Hall of Famer sat out of Friday's game against the Twins, but was back in on Saturday, to Ron Gardenhire's dismay.
"I asked Mr. [Joe] Girardi over there today ... to take you out of the lineup for two more days and we'll be fine here in Minnesota," the Twins' manager told Jeter in jest during the ceremony.
"It's been an honor and a pleasure to share this field with you. We wish you nothing but the best. We have total respect for you and what you represent in the game."
After the game, which the Twins won, 2-1, in 11 innings, Jeter returned the compliment.
"I've always had the utmost respect for Ron Gardenhire, and for him to say those things about me before the game, it's something pretty special," he said.
Alex M. Smith is an associate reporter for MLB.com. Follow him on Twitter @asmiff. This story was not subject to the approval of Major League Baseball or its clubs.