U might want to provide more details about your 'sparephone' if u want help. Like the Brand atleast.
SIM has a limited memory and can store upto 250 contacts. It can also store around 20 SMS as well.
You can try exporting the contacts to .csv from your Nokia phone.
Contacts > Settings > Export > Store in SD card.
And later transfer the .csv file to new phone through Bluetooth / USB (If supported).
If .csv is not supported on your phone. You might have to convert this .csv file to .vcf contact files and try importing.