What is best way to reject candidate referred by highly-valued employee?

Directly, with a tactful, yet honest approach. Assuming your reasons for rejection are valid, articulate them in a compassionate way. Lying to a candidate to spare their feelings doesn't help them at all.

I refer a lot of friends who may or may not be qualified. Often I love their attitude and they're impressive in some way. But that doesn't mean they make the cut. I always tell people to run them through the full gauntlet whenever I refer someone.

The easy way to figure it out is to take the decision to the referrer and have them appeal it. Sometimes the rejection decision is justified. Someone has good technical skills but poor fundamentals. Sometimes it's a mistake - the person sounded unenthusiastic, but it's because they were sick or going through a parent's death. Often it's pretty accurate and you can show respect for the referrer by cross checking with them.

Like others have mentioned referral doesn’t mean acceptance… be direct with rejection.

If it’s a demand,then you have a dicey situation to deal with… I once had a highly-valued employee try to “forcing” me to hire the brother. I resisted, things got weird and he eventually left - which was admittedly painful but it would have been doubly painful had I given in to the demand.

Quickly, and honestly. I've been both sides of this, and there is a pain around the lingering death of a fail.

Recommending/Referring isn't pre-clear for flight. People can be wrong about their friends.

Like any other candidate. Referrals still have to go through the same process.