Yes. Generally, the most travel insurance policies will provide refunds if you are within the “free look” period which is usually 10 to 15 days after purchase of the policy.  Sometimes a small administartive fee of $5 – $8 is not refundable.  Travel Medical policies usually provide refunds as long as you have not departed, have not filed a claim or if you have sent a written request prior to the policy’s effective date.