I met up with some old friends today. We spent the afternoon reminiscing. or I met up with some old friends today. We spent the afternoon reminiscing about our schooldays. As you can see, 'reminisce' can be used on its own, as in the first sentence. Alternatively, you can mention the subject of your reminiscences: in this case, the correct construction is 'reminisce + ABOUT + something'.

He was reminiscing the joys of his childhood. Reminiscing the good ol' days is not part of his character.

Thanks J.Luke

Little River Band: "Reminiscing" Hurry, don't be late I can't hardly wait I said to myself when we're old We'll go dancing in the dark, walking through the park And reminiscing