It's also worth noting that in the Roman time period you're specifiying, the meritocracy as you call it was probably a result of circustance rather than a cultural or political movement that embraced a more technocratic outlook.

Augustus for one, wanted to leave the Empire in the hand of his direct family...but his family had a bad habit of dying. Tiberious, while worthy to take the job based on merit (you can argue how well he did as Emperor, especially in the later years but he was a distinguished solider/statesman) but Augustus did not think about appointing him into he was the only choice.

Most (all?) of the Emperors in the five good emperors period did not have living or capable sons when they needed them. Adopting heirs was a tradition in Rome, so the Emperor got to choose. We can at least give them credit for making some good choices though.

If they had healthy, adult children when they needed them, the Emperors would likely have chosen their biological heirs to take over.

This is a fun question!

First, a note on terminology. Empires are not necessarily headed by emperors, even in the Roman Empire. The so-called Five Good Emperors would not have thought of themselves as "emperors" in our sense of the term. The title they used was princeps. Further, what makes an empire itself is open to significant debate. Generally speaking, some form of hegemony of one group or polity over another is required, but that's about it. The governing system of the ruling polity does not need to be autocratic at all. In fact, Rome itself was ruled via republican institutions for some 150 years before the death of Julius Caesar while still very much being an imperial power in the Mediterranean. Further, what if the otherwise autocratic leader of the imperial state is not called an emperor (or one of its obvious translations), surely that would count, no? Finally, what do we want to mean by "appointment through merit"? Must it be the outgoing ruler who chooses the replacement, or can that replacement be chosen by some other person/group? I'm not entirely sure that the Five Good Emperors even hand picked alone their own respective replacements without at least some pressure from outside groups. Nerva, for example, I'm pretty sure was overtly pressured to choose the wildly popular Trajan as his successor, while Antoninus Pius was appointed as a stop gap for the then-still-too-young-but-destined-for-the-purple Marcus Aurelius.

I would argue here that the most obvious example of a similar peaceful transition of nearly absolute power among imperial states would be the Soviet Union, post-Stalin, and the current day People's Republic of China. Both governments rule(d) autocratically with supreme power very highly concentrated, both had multiple peaceful transitions of power based, more or less, on merit (I'll grant that the question of what was meritorious was certainly different in each society, but still), and both states were openly imperial in actions (Eastern Europe, Central Asia, Tibet, etc.), if not in ideology/ethos.

If you want to move into less autocratic, more democratic forms of government, you can look at the United States, which is an imperial state by almost any definition. The US has managed, with only a few hiccups, to transition leaders peacefully something like 40 times in its history, with most transitions determined by merit, as determined by the voting electorate. Presidential power isn't absolute, of course, nor do Presidents often successfully pick their successors, but it's not unheard of either.