Aside from papal miters and tassel bedecked hats, we have crowns for nobility or families with ‘royal connections’ that reach beyond the Italian borders. How does this come about — marriage, bargaining chips, and favors too. Take the Aldobrandini family crest: not only was there a pope in Clement VIII Aldobrandini, but there were also cardinals and somewhere along the line ‘arrangements’ where made that finds the family with their seal surmounted by a crown, signifying royalty. This coding does not require a specialization or scholarship in family crests, popes or cardinals or specific names, necessarily. The decoding is an overview based on the visual ‘hieroglyphics’ as presented.  

Now to highlight specific families:

PICCOLOMINI

Let's take the Piccolomini family from Siena, as well as heirs to a town in Tuscany which they renamed ‘Pienza.’ The town of Pienza was totally reconfigured and the main piazza is one of the great, early Renaissance displays of an ideal town plan. The Palazzo Piccolomini which defines one edge of the piazza displays both the cardinal's hat and the papal miter with either or both placed above the Piccolomini cross and half-moons. Decoding here is simple: we are being told that Pius II Piccolomini (1458–1464) was first a cardinal and then the Pope. This could mean that the palazzo was under construction while he was a cardinal and completed after he was elevated to Pope.  

The family is identified by a blue cross with five half-moons, thus their family seal. The Palazzo Piccolomini defines one side of the trapezoidal piazza in Pienza and displays the family stemma over its main entrance(s), and more prominently, a stemma is attached midway up the palazzo’s corner. Corners are all-important, because a corner and, therefore, a stemma, can be viewed from more than one vantage point.