OK, here's an idea--we send out a ship to world that's 100 light-years away; the ship travels at 1/10 the speed of light, and will take 1000 years to get where its going, so they aim at where the star will be in 1000 years time, and plot their course accordingly.
100 years later the technology has advanced to the point where ships can travel at 50% of the speed of light, and one such ship goes out to the same star. The crew aim the ship at where the star is going to be in 200 years time, and plot their course.
They could deviate their course to pick up the crew and passengers of the first ship and help them get to the star-system in the shorter time.