Bastions of tradition are trembling. The Old School members are turning over in their graves. For the sipping of aromatic and flavorful liqueurs from snifters while sitting in a cushy wing-back chair is a dying art.

That doesn’t mean cordials and liqueurs are dying, though. Far from it. In combinations that may make purists shudder, cordials are more popular than ever as featured ingredients in mainstream Martinis and Margaritas.

Places like New York’s famous Rainbow Room still serve Manhattans, Sidecars and after-dinner liqueurs. But rather than a Bellini — invented at Harry’s Bar in Venice, whose owners, the Cipriani family now run the Rainbow Room — trendy establishments now are more likely to serve a Bellini Martini, using peach schnapps as an ingredient.

One of the drinks featured recently at the T.G.I. Friday’s chain is the “Blue Storm,” a concoction Southern Comfort, blue curacao, peach schnapps and pina colada mix.

The Bennigan’s chain just introduced a new stand-alone beverage and dessert menu that features about 30 specialty drinks, most flavored with some sort of cordial. The chain’s “Patio Punch” is a tropical drink containing Midori, Malibu, blue cura