Several reputable universities and platforms offer free online courses in neuroscience and neurology that provide certificates upon completion. Here are some options:

1. **Harvard University – Fundamentals of Neuroscience**

- A three-part online course covering neuron properties and brain functions.

- Free to access, with an optional paid certificate.

2. **Coursera – Neuroscience Courses**

- Courses from top universities, available for free audit.

- Certificates available with payment or financial aid.

3. **edX – Neuroscience Programs**

- Courses from institutions like Harvard and MIT.

- Free to audit, with an option to pay for a verified certificate.

4. **Alison – Introduction to Cognitive Neuroscience**

- Free course with a no-cost certification upon completion.

5. **Class Central – Neurology and Neuroscience Courses**

- Aggregates free neuroscience courses from various universities.

- Some courses offer free certificates, while others charge a fee.

6. **British Neuroscience Association – Online Courses & MOOCs**

- Lists various free neuroscience courses, some with certificates.

Many courses are free to access, but certification may require payment. It's advisable to review course details before enrolling.