Jorudan seems to require a paid log-in to specify limited express results, and it won’t give you a list of all the limited express trains from one city to another, all day long. I have not found an English route finder that will, although there might be one. I have found Japanese-language route finders that will, but they require a certain level of proficiency in Japanese. And the best one I have found is a paid subscription.
When I want to quickly find a full list of limited express trains between two cities, I use JR Cyberstation. This is not a route finder, but rather a seat availability checker. So it is not good for finding the best route between two cities. It will, however, tell you if there are any limited express trains, and if you set a time early in the day you can get a list of every single one of them. (Then you can go about getting seat reservations.) Note that it is not available late at night Japan time; I think the hours it is available are between 6 a.m. and midnight.
To identify the LEx trains between Kyoto and Himeji with Cyberstation, select Available Seats, then choose Conventional Lines to rule out Shinkansen lines, type Kyoto and Himeji into the boxes and make sure they are accepted, and choose a time early in the day.
https://www.jr.cyberstation.ne.jp/index_en.htmlApparently there are some Shin Kaisoku trains with reservable seats between the two cities, as well as the two morning departures of the Super Hakuto. And a 7:35 p.m. train called the Raku-Raku Harima, whatever that is.
When I have an active JR pass I often use limited express trains for short hops in urban areas (in particular between Kyoto and Osaka but sometimes also in Kanto), and Cyberstation is the tool I usually use to find what is available. If there is a better English-language tool I would like to know about it. Unfortunately, Cyberstation will not tell you if a given limited express train has unreserved cars, and also unfortunately, a lot of LEx trains are becoming all-reserved only, so just hopping on without a reservation is no longer an option for those trains.