How to enforce an "exactly-one-per-group" constraint?

I have a table x that I've defined like this:

CREATE TABLE x (
    xid INTEGER NOT NULL PRIMARY KEY,
    yid INTEGER NOT NULL REFERENCES y(yid),
    is_principal BOOLEAN NOT NULL
);

This definition misses one constraint that x must satisfy. In English, this constraint could be described like this:

there may be one or more rows with a given value in the yid field, but among them there must always be exactly one whose is_principal field is TRUE¹.

I'm looking for a way to enforce this constraint.

(In case it matters, I'm particularly interested in solutions applicable to SQLite3 and PostgreSQL.)

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_{¹ Another way to express the same constraint would be to say that the following two queries should always produce identical outputs:}

SELECT DISTINCT (yid) FROM x                    ORDER BY yid;
SELECT           yid  FROM x WHERE is_principal ORDER BY yid;