Frida performed in Charlie Norman's show and was filmed performing (Frida performances are in bold):

1. Charlie Norman at the piano
2. Lilla Frun with Mona Thelmée
3. Charlie Norman sings with Lennie Norman
4. Spara och slösa (Love & Marriage) with Mona Thelmée
5. Charlie Norman at the piano
6. Hasse Burman
7. Mona Thelmée
8. Bäbi läv (Baby Love)
9. Minns oss- Frida and the rest of the artists on the show

Other participants in the shows were Hasse Burman and Lennie Norman.

See here for a magazine article about the Charlie Norman show including a couple of pictures of Frida (sorry but the quality is not good enough to see the text).

(NB. The clips broadcast on Essential Stockholm (VHS only) state that these clips are from 1969, yet the Frida Box Set information states they are from 1970. I am going with the official product's year of 1970.)

The whole Charlie Norman Show was released on the SVT Open Archive but has since been removed.

This cutting indicates that the programme was also broadcast on 27 December 1970 but there are no such TV listings for it on that day.

Click here for a TV listing from Arbeiderbladet - 11 April 1970, p.15.

Segments of Spara och slösa were broadcast on Diggiloo in early 2000s, while Bäbi läv was included in the Frida Box Set released on 5 December 2005. The other clips have not been included on any officially released video or DVD.

Charlie Norman Wikipedia page; 

Charlie Norman show / med Annifrid Lyngstad, Mona Thelmée, Hasse Burman samt Charlie Normans kvartett
Stockholm : SR, TV1, 1970-04-11 20.40-21.10

Namn
Personer Kåge, Sigurth (producent)
Norman, Charlie , 1920-2005 (medverkande)
Lyngstad, Anni-Frid , 1945- (medverkande)
Thelmée, Mona (medverkande)
Burman, Hasse (medverkande)
Norman, Lennie (medverkande)

Utgivning
År/datum 1970-04-11 20.40-21.10
Kanal SVT1
Utgivning Stockholm : SR, TV1
Utgivningsland Sverige
Originalformat
Originalets nummer V07.605 ; V01.549

Arkiv
Leverantör SVT TVARK

Exemplar
MPEG-1 XA_TF07-0386

Ljud mono
Filbeskrivning 1,5 Mbit/s, MPEG-1 layer 2, 48 kHz, 128 kbit/s

Arkivnummer XA_TF07-0386

Thanks to the makers of the Essential Stockholm video, Steve Layton, Marcus Bergs, Pepe Toransocalderon, Robin Andersson, Tony Rogers c/o ABBAtalk and Jozsef.
Thanks to Carl Magnus Palm for the filming date and location.
YouTube link c/o inomadi100