LEWISTON — Look up the Glenn Miller Orchestra on the Internet and you may find out that Glenn Miller Productions licenses the name. The current branded American outfit made a trek all the way from the Fredonia Opera House, where it played a gig Sunday, to Artpark for a pair of shows there Monday. Given its packed touring schedule, this Western New York trip could almost qualify as a “piece of cake.”

It is fairly easy to draw comparisons between the American Glenn Miller Orchestra and how it treats Miller’s heritage with groups like the Dark Star Orchestra (a cover band for Grateful Dead fans) and individuals impersonating Elvis Presley. They all seek to grab onto the mystique associated with artists, re-creating songs and styles for generations who remember the originals and those who don’t.

The Glenn Miller Orchestra does a really credible job of recreating a musical era, but it also manages to incorporate a mix of songs by other bandleaders from that time period with a few recent items tossed in for freshness. The band itself is filled with solid musicians who’ve been coached in the Miller manner by the group’s musical director, trombonist Larry O’Brien.

They often run through moves drawn straight from the playbook of swing band choreography. You had the trombone section standing and sweeping back and forth with its slides rippling the air, causing brief, purposeful hindrances for the trumpeters trying to get to the microphone for solo spots. The trumpeters engaged in their own semicomedic visual effect by using their mutes as hats, while the Moonlight Serenaders (a vocal quintet) often took part in genteel mugging between and during choruses.

As expected, the set lists were geared toward maximum familiarity. After the opening strains of Miller’s theme song, “Moonlight Serenade,” the orchestra eventually mined the bandleader’s catalog of hits for “Little Brown Jug,” “Tuxedo Junction, “(I’ve Got a Gal in) Kalamazoo,” “String of Pearls” and “Fools Rush In (Where Angels Fear to Tread)” as varying numbers of dancers swung their way around the dance floor in front of the stage.

Standards associated with Duke Ellington (“In a Sentimental Mood”), Artie Shaw (“This Time the Dream’s On Me”) and other veterans of the big-band era actually revealed more about individual band members’ talents than the Miller classics did. O’Brien’s solo in “Body and Soul” was smooth as silk, and the tenor saxophone riffing in “Limehouse Blues” from Damian Sanchez was one of the concert’s real highlights despite its brevity.

Concert Review

Glenn Miller Orchestra

Monday night at Artpark Mainstage Theater.