You can check your sending IP reputation by finding your primary IP for email sending and using third-party tools such as Google Postmaster Tools, Sender Score by Validity, Talos Intelligence by Cisco, BrightCloud's IP List, or MultiRBL. These tools provide insights into your IP's reputation across different receivers, including inbox providers like Gmail, and help you identify potential issues that may impact deliverability. By regularly checking and maintaining a good IP reputation, you can improve the likelihood of your emails reaching inboxes quickly and reliably.