My family and I were proud and pleased to see the judge walk across the ring to shake my hand.

How to make this a compound-complex sentence?

My family and I were proud and pleased to see the judge walk across the ring to shake my hand, and we knew that our hard work and dedication had paid off, even though we hadn't won first place.

To make the sentence "My family and I were proud and pleased to see the judge walk across the ring to shake my hand" a compound-complex sentence, we can add an independent clause and a dependent clause.

Here's one way to do it:

"Although my family and I were proud and pleased to see the judge walk across the ring to shake my hand, we were also relieved when he announced our victory."

In this example, the dependent clause "Although my family and I were proud and pleased to see the judge walk across the ring to shake my hand" adds additional information about the speaker's feelings. Meanwhile, the independent clause "we were also relieved when he announced our victory" introduces another thought and completes the compound-complex structure.