You could align the text in both frames to a baseline grid. Or you could only use increments of paragraph space-before and space-after that will work with your leading, but I find that the baseline grid is a quick & easy solution.
Sorry, forgot to mention I do align it to the baseline grid. But it doesn't end up ending in the same baseline.(I don't know if this is even possible I just wanted to see if anyone knew if it was.)
Do the frames contain the same number of lines? If not, you probably want to rethink, turn OFF align to grid, and set the the vertical justification to Justified in the Text Frame options.
Personally, I think this is a bad look, though. If you tell us more about what you are really doing, it would help.
Maybe you should ask your question with some more details, or maybe a screenshot.
Are you trying to balance two colums of text so they both have the same number of lines? That is doable, assuming that you have an even number of lines of text. If you have an odd number of lines, then you need to change your text somehow to force an even number of lines, by changing column width, tracking, copy editing, word spacing, et cetera.
I've never used "Balance Columns" functionality of InDesign, and by all reports it is a major performance hit, but there is a tool that does this automagically - check the help.
Try this: set the two boxes to the same size. There's no problem if are not the same lines in boxes.
After that go to "Object / Text frame options", Vertical justification: Align = Justify.
So the two text boxes that are linked will end on the same baseline .
Sorry it's hard for me to describe and at the moment I don't have a screenshot as I don't have access to the file. Basically what I have is a letter of information describing a place. It's made up of two text boxes that are linked that I drop into a grid to break things up into columns. However the next text box ends earlier than the other one I am trying to have it where they end on the same line. I don't know if my description made it more confusing. But thank you guys for answering my questions. You guys have been really helpful!
Soundsl like you'd be better off with a two-column frame and balancing columns.