welcome to Worldbuilding!
OK, I'm going to assume tech level of ours or higher, and that you have access to whatever you want (hey - you can go to different worlds, mere baubles are easy!)
So, we're going to need at least 3 atomic clocks (slight problem, they aren't exactly pocket watch size, but let's hand wave that minor issue!). We probably don't really need the level of accuracy here, but let's go for the platinum solution.
The 1st clock we leave in reality 1. It's our "base time" if you will.
Clock 2 goes to reality 2, along with clock 3 which is the one we lug around with us wherever we go.
So, we have an an accurate time piece in both realities, and a clock we're lugging around too.
We now need to start going back and forth between the 2 realities. Obviously, we need to go between our 2 fixed clocks. I'm not sure how many travels we'd need - I vaguely remember 5 data points for a line graph, but more would be better (depending on the time differential, this may be a multi-generational project!). We then try and correlate the differences, possibly seeing if there's a travel time going between the realities with clock 3.
Simple really... :P