I'm not totally convinced this isn't a problem for learners of any language, not specifically German, but it does seems worthy of an answer so I'll do my best anyway.
First, I'm not really sure what these things are called. When it involves a verb then I've seen "prepositional verb" used, but this can be misleading because there seem to be two different types in English, one of which corresponds to separable verbs in German one which corresponds to other phrases in German. In English you can tell the difference because in the first type the preposition is moved after the noun, as in "you woke me up" while "you woke up me" is incorrect. These correspond to separable verbs in German and the similarities are no doubt due the common ancestry of the two languages. In the second type the proposition stays in front of the noun, as in "you trusted in me" while "you trusted me in" is incorrect. The grammar here in both languages is the same as for any other use of a preposition, but the phrases carry a special meaning different from their literal meaning. When you include such phrases involving parts of speech other than verbs then I'm tempted to refer to them as "prepositional phrases", but it seems that's already being used for any phrase that involves a preposition whether it has a special meaning or not. I'm reluctant to call them "idioms" because to me that term should be restricted to figures of speech with more than one content word, thus requiring a separate dictionary entry.
So, as you might have guessed, I'm familiar with the phenomenon you're referring to. But the question was whether there is a place to look these things up. I can offer some suggestions but AFAIK there aren't any really good places to do this. DWDS does have this information most of the time. For example in their entries for richten and stehen there are sections marked mit Präposition (or something similar) and then subsections marked Grammatik: in Verbindung mit ... for individual prepositions. But DWDS doesn't always include this information, or if it does it's not in a format that's as easily recognizable. For example in the entry for sehnen, its use with nach is shown in a kind of label in front of the main definition. English Wiktionary often uses this kind of labeling system as well, for example see sehnen on that site.
Another place to find this information is dict.cc, since they include many multi-word combinations as well as single words. They give word for word translations instead of definitions though, and that can be confusing at times. You might also try Redensarten-index, which translates to "Figures of speech index". They tend to cover idioms and more general figures of speech.
IMO every learner of German should be familiar with these sites in any case. It seems that there is no single source that covers everything you need to know, so it's good to have a "go to" list of places to look for various types if information.
