The phrase "tortoise's paces" refers to a slow and steady speed. Synonyms for this phrase include "snail's pace," "crawl," "plod," "creep," and "amble." These words all imply a leisurely or cautious movement. Other synonyms for a slow speed that may not have the same reptilian connotation include "saunter," "meander," "shuffle," and "lumber." It's important to select the right synonym based on the context of the sentence, as each word can have its own subtle nuance or connotation. Regardless of which term you choose, they all describe a slow and steady pace that can be useful to describe certain situations or characters.