When is the best time to travel to Spain and Portugal?

For Spain at least, it will be difficult to predict the tourism crowding situation in a post-pandemic world, but pre-pandemic there was no "off season" for most of the major cities/sites like Barcelona/Sevilla/Madrid/Alhambra. Weather-wise however, the rule of thumb is February - May anywhere south of Madrid, and June - November anywhere north of Madrid. December/January are tricky due to the unpredictability of the weather.

I was in Spain in late Oct/early November, from Granada, Seville, to Madrid and Segovia. By Nov 11, Segovia had already had their first snow flurries (not staying however), and Madrid required gloves and a hat. Weather was still great, but I do know the year I went was out of the ordinary in that it was still drought conditions. Normally it would be rainy season. That being said, the only place I thought might have been considered crowded was the Alhambra in Granada. It was also a Sunday so there were locals as well as bus tours. It was nothing like it would be height of summer, however, and I was in sandals and sleeveless in the afternoon late October. I also kept a slower pace, so the bus tours would move out of the way faster than me. It only got to be a bit of a bottle neck at the Generalife palace, which is a small part of the entire grounds. I made sure to have an early booking for the Nasrid Palace, so beat the groups; and they do limit numbers, so all manageable. My limited time in Portugal was over Christmas. Weather wasn't ideal, but a lot warmer than my Canadian home town and there were breaks so when we were on the coast, it was actually sunny and pleasant.
All that being said, you would be dependent on when the tours are offered. April and October could work, but know that there are a number of festivals in Spain in April, so it could local participation might make things busier.

I would opt for May, early June or September when the weather should be ok and daylight hours are longer. The major cities are busy year round. April means Easter, which will be busy and school holiday time.

I have been to southern Spain in February and March and had some ok weather, but also bitterly cold and wet.

We spent 5 days in Granada in mid-November 2019. It seemed very crowded on the weekend. We took a Segway tour and asked our guide about the crowds. He said it WAS really crowded, but it is EVERY weekend in Granada. Many of the small alleyways were packed with people. I remember saying to my husband, “I can’t imagine this place in summer!”

The heat would dictate my travel dates. I’m not a fan of being crowded AND hot. I would look at tours in October. Weather should be pleasant, and the days relatively long.

adding to others who mentioned the fall for Spain, our last trip, which was Madrid and points north, was in October a few years ago. Places like Barcelona still had many other tourists, but it wasn’t overwhelming. Other places were almost empty. We had decent weather almost the entire time, except for 2 soggy, rainy days on the northern coast, in San Sebastián.

The last trip to Portugal was in June even longer ago. Not horribly crowded, and getting hotel rooms was easy. Maybe that’s changed in the ensuing years, and depends on where you’re going.

Coming out of the pandemic could mean slow reopening, or a mass rush of pent-up travelers taking advantage of bargain prices. Are you normally free to travel any time, or is your schedule limited to certain months? Do you have any tour providers in mind, and can they offer suggestions as to when they’re less busy?

In recent years, I've traveled to "southern" Spain - Madrid, Barcelona and points south - in February and March. The only times I encountered crowds were during festivals and then only at certain times or in certain places. The weather was mild (50s-60s), mostly sunny. I was in Portugal in 2019 mid-May to early June, and there weren't crowds at all except in Sintra.

It snowed and later heavily rained when I was in Madrid for a couple of days in early February, 2018. I had been there before in warm weather, so it was certainly interesting to see things with a layer of snow. I was in Barcelona for a week in March, 2019 and the weather was warm enough for a light to medium jacket most days and while there were still crowds, it wasn't as crowded as when I visited there in September, 2017.

We have had two wonderful trips to Madrid and Andalusia in late October early November after the heat was gone. Beautiful weather.
We have been in Barcelona and the Basque region in June and early July, no issues with heat there at that time.
Portugal had a wonderful trip exploring the whole country independently in June.