I'm making an assumption about your world: that it's rotating in reverse. Note my comment to your question. However, what I have to say works regardless of rotation, you just need to keep all the directions in mind.
Climate is complex (really complex...) and we must necessarily simplify it to achieve success. Reversing Earth's rotation means, primarily, that the planet has prevailing easterly trade winds rather than prevailing westerly winds. A great deal changes with that, including where rivers and lakes are prominent, how currents flow, etc., and that's messy complex, but let's start with the easterlies.
Your goal is to let warm, moist air deeper into the areas you're interested in. That means mountain chains (and, therefore, tectonic plates... complex!) that favor the western areas of your continent(s), leaving the eastern areas flatter and more prone to letting storms move inland.
But on top of that is the gulf stream. This is an ocean current that draws temperature-moderating water (and wind along with it) to areas that would otherwise bet too hot or too cold. Frankly, a lot of Earth's habitability relies on the gulf stream. As you design your world you'll need an eastern-flowing "gulf stream" that channels warm, equatorial waters into northern areas. This will affect the shape of some of your continents.
Finally, consider continental drainage. The idea of "goldilocks zones" extends from landscaping to astronomy and the phrase describes the "perfect area" for life. You need water drainages that don't drain too fast or too slowly. Geologically, this usually means old basins where rainfall has moderated slopes and increased the amount of sedimentary soil in the basins before water is collected and returned to the ocean. You need some "downhill" to let the water move or you end up with swamps and not too much downhill or you'll end up with canyons. This has a lot to do with the type of rock in various areas (complex!).
Finally, a great deal of what makes the Mediterranean climate the way it is, is, frankly, the Mediterranean sea — a central, somewhat shallow body of water that "holds the heat" and regularly evaporates water for rain in surrounding areas. Oversimplifying to the point angels weep, you can do this in two ways: one is the way Nature developed with a single body of water. Consider the surrounding countries: lush and bountiful, but arid.
The second way to do that is to distribute the sea as a region of lakes. Lush and bountiful, but soggier. Probably a bit cooler, so you'd need to distribute less than the sea to balance it out. The region would need higher rainfall to keep the lakes filled. Thus, soggier.
