The two verbs have slightly different connotations, but they can often be used interchangeably.
As you said, “sądzić” is usually used to talk about passing judgement. It’s not that hard to see when you look at words such as “sąd” (“a court” [of law]) or “sędzia” (“a judge” / “a referee”), which are both closely related to “sądzić”.
“Myśleć” is a more generic word, and mostly corresponds to the verb “to think” in English.
Here are some contexts where the two words can be used interchangeably:
Sądzę/Myślę, że to on jest mordercą. (“I think that he is the murderer.”)
Co o tym sądzisz/myślisz? (“What do you think about it?”)
O czym myślisz? (“What are you thinking about?”)
Myślę o pierogach. (“I’m thinking about pierogi.”)
In both these examples “thinking” refers to a continuous process, and not to the fact of having an opinion on something—this is why we can only use “myśleć”, and not “sądzić”. As I’ve said, “sądzić” is usually related to having an opinion on something.
Nie sądzę. (“I don’t think so.”)
This is probably the only idiomatic way of saying this. Using “myślę” here would suggest that you’re incapable of thinking.
In general, negations corresponding to the English “I don’t think that…” will usually use “sądzić”, and not “myśleć” (-> “Nie sądzę, że…”) .